TSIA2- Chapter 6 – Geometric and Spatial Reasoning – Question Set 2

#1. (4, 4) reflect y-axis. New?

(-4, -4)

(-4, 4)

(4, 4)

(4, -4)

#2. Rectangle 24 m × 7 m. Diagonal?

48.5 m

25 m

17 m

31 m

#3. Chord 24 cm in circle radius 13 cm. Distance from center to chord?

11 cm

7 cm

12 cm

5 cm

#4. Cylinder radius 4 m, height 6 m. Volume? (V = πr²h, π ≈ 3.14)

226.08 m³

150.72 m³

301.44 m³

75.36 m³

#5. Rotate (-1, 2) 180°, origin. New?

(1, -2)

(2, -1)

(-2, 1)

(-1, 2)

#6. Cone diameter 12 cm, height 10 cm. Volume? (V = 1/3 πr²h, π ≈ 3.14)

376.8 cm³

141.3 cm³

188.4 cm³

753.6 cm³

#7. Two similar triangles have sides in ratio 2:3. Smaller has perimeter 20. Larger’s perimeter?

60

30

40

13.33

#8. Isosceles right triangle legs 6 cm. Hypotenuse?

6 cm

12√2 cm

12 cm

6√2 cm

#9. Cities (12, 18), (15, 22) on map. Distance?

7

√34

3

5

#10. Square with area 49 sq cm. Perimeter?

196 cm

49 cm

28 cm

7 cm

#11. Rectangle 24 ft × 16 ft. Perimeter?

384 ft

80 ft

60 ft

40 ft

#12. Dilate (9, 12) scale 1/3, origin. New?

(1, 1.33)

(27, 36)

(3, 4)

(9, 12)

#13. Isosceles triangle lines of symmetry?

2

1

0

3

#14. Trapezoid lines of symmetry?

1

0

4

2

#15. Horizontal through (5, 7). Equation?

x = 5

y = 7

x = 7

y = 5

#16. In a 30-60-90 triangle, the shorter leg is 5. Hypotenuse is?

5√3

5√2

15

10

#17. Vertical angles: one is (2x + 24)°, the other is (5x – 9)°. Find x.

13

11

9

7

#18. Isosceles trapezoid bases 28 m, 18 m, legs 11 m each. Perimeter?

74 m

68 m

57 m

46 m

#19. Cone radius 3 m, height 9 m. Volume? (V = 1/3 πr²h, π ≈ 3.14)

169.56 m³

84.78 m³

254.34 m³

42.39 m³

#20. Vertical angles are formed by two intersecting lines. If one vertical angle measures 42°, what is the measure of the angle adjacent to it?

84°

138°

90°

42°

#21. Distance (0, 5) to (12, 0)?

17

8

13

7

#22. Square perimeter 52 cm. Side?

4 cm

26 cm

13 cm

169 cm

#23. (5, 5) move 2 right, 2 right. New?

(7, 5)

(5, 9)

(9, 5)

(5, 7)

#24. Rectangular prism 12 cm × 8 cm × 5 cm. Volume?

240 cm³

480 cm³

200 cm³

960 cm³

#25. An isosceles trapezoid has legs of 7 in and parallel bases of 9 in and 15 in. What is the perimeter?

31 in

46 in

52 in

38 in

#26. Corner (3, 8) translate 4 up, 1 down. New?

(3, 7)

(1, 8)

(7, 8)

(3, 11)

#27. Dilate (10, -8) scale 0.5, origin. New?

(20, -16)

(10, -8)

(5, -4)

(2.5, -2)

#28. Cone radius 5 cm, height 12 cm. Volume? (V = 1/3 πr²h, π ≈ 3.14)

628 cm³

314 cm³

942 cm³

157 cm³

#29. Shape corner (8, 5) move 2 left, 4 up. New?

(10, 1)

(10, 9)

(6, 9)

(6, 1)

#30. Endpoints (5, 1), (1, 5). Midpoint?

(4, 4)

(2, 2)

(6, 6)

(3, 3)

#31. Rotate (2, 3) 90° clockwise. New?

(-2, 3)

(2, -3)

(3, -2)

(-3, 2)

#32. (-8, 2) reflect y = x. New?

(8, -2)

(2, -8)

(-2, 8)

(-8, 2)

#33. Translate (1, 1) by . New?

(4, -1)

(-2, -1)

(4, 3)

(-2, 3)

#34. Two concentric circles: radii 6 and 3 cm. Annulus area? (A = π(R² – r²), π ≈ 3.14)

113.04 cm²

84.78 cm²

28.26 cm²

254.34 cm²

#35. Circular flower bed radius 3.5 m. Edging needed? (C = 2πr, π ≈ 3.14)

11 m

7 m

22 m

38.5 m

#36. Congruent triangles by SAS: two sides 12 and 18 with included angle 60°. Perimeter 50. Sides are?

10, 18, 22

12, 15, 23

12, 18, 20

14, 18, 18

#37. A kite has two pairs of adjacent equal sides: 6 cm, 6 cm, 11 cm, 11 cm. Perimeter?

66 cm

28 cm

34 cm

17 cm

#38. Midpoint (2, 8) to (6, 14)?

(3, 7)

(4, 11)

(2, 3)

(8, 22)

#39. Arc length 15.7 cm with radius 5 cm. Central angle? (arc = θ/360° × 2πr, π ≈ 3.14)

360°

45°

180°

90°

#40. Two points (6,8) and origin. Distance?

10

2

14

48

#41. In a right triangle, the acute angles measure 31° and x°. Find x.

62°

31°

149°

59°

#42. Distance (-6, 0) to (0, 8)?

10

14

8

2

#43. Pentagon regular, side 6 inches. Perimeter?

24 in

36 in

12 in

30 in

#44. Reflect (-1, 3) over x-axis. New?

(-1, -3)

(-3, 1)

(3, -1)

(1, 3)

#45. Two triangles satisfy the ASA congruence criterion. Triangle ABC has angles 52° and 63° with included side 14 cm. What is a corresponding angle in Triangle DEF?

127°

31°

65°

52°

#46. Four angles meet at a point around a circle, totaling 360°. Three angles measure 85°, 92°, and 73°. What is the fourth?

110°

120°

100°

130°

#47. y-intercept 2x + 5y = 10?

5

2

-2

-5

#48. A carpenter finds that two supplementary angles measure (3x + 15)° and (2x – 5)°. What is the value of x?

28

34

36

32

#49. Rhombus diagonals 14 cm, 20 cm. Area?

34 cm²

140 cm²

280 cm²

200 cm²

#50. A right isosceles triangle has legs of 8 inches. What is its perimeter?

32 in

16 in

24 in

16 + 8√2 in

#51. Rectangle sides 9 and 12. Diagonal?

√225

15

21

3

#52. (0, 4) rotate 90° clockwise. New?

(4, 0)

(-4, 0)

(0, -4)

(0, 4)

#53. Regular hexagon side 12 cm. Perimeter?

60 cm

144 cm

36 cm

72 cm

#54. Semicircle radius 8 m. Perimeter? (includes diameter)

8π + 16

16π

24 + 8π

8π + 8

#55. Slope through (1, 2), (4, 8)?

2

-2

3

1/3

#56. Semicircle radius 9 inches. Area? (A = πr²/2, π ≈ 3.14)

63.59 in²

81 in²

127.17 in²

254.34 in²

#57. Endpoints (0, 0), (12, 8). Midpoint?

(12, 8)

(6, 4)

(0, 0)

(4, 6)

#58. Point (-1, 3) translate 5 right, 0 up. New?

(-6, 3)

(4, 3)

(4, 8)

(-1, 8)

#59. Distance (2, 2) to (5, 6)?

√34

5

3

4

#60. Triangular sail base 8 m, height 6 m. Area?

24 m²

48 m²

28 m²

14 m²

#61. Vertical line slope?

undefined

1

0

-1

#62. Two supplementary angles have a ratio of 3:7. What is the measure of the larger angle?

126°

90°

108°

54°

#63. Trapezoid bases 15 cm, 23 cm, height 8 cm. Area?

184 cm²

304 cm²

180 cm²

152 cm²

#64. Segment (-1, 5), (3, 1). Midpoint?

(1, 3)

(2, 6)

(2, 3)

(0, 2)

#65. Points (0, 3), (2, 7). Slope?

1/2

-2

-1/2

2

#66. Rectangle corner (0, 0), translate 6 left, 3 up. New?

(6, -3)

(-6, -3)

(-6, 3)

(6, 3)

#67. Rotate (3, 0) 90° clockwise. New?

(0, 3)

(3, 0)

(-3, 0)

(0, -3)

#68. Triangular playground 27 m, 35 m, 19 m sides. Perimeter?

162 m

81 m

92 m

46 m

#69. Dilation scale 3: area becomes how many times larger?

27

9

3

6

#70. Rotate (-3, 5) 90° counterclockwise. New?

(-5, -3)

(-5, 3)

(5, 3)

(5, -3)

#71. (0, 0) translate . New?

(0, 0)

(8, 4)

(4, -8)

(-4, 8)

#72. Points (8, 2), (3, 2). Slope?

undefined

-1

1

0

#73. Rotate (0, -8) 90° counterclockwise, origin. New?

(8, 0)

(0, -8)

(0, 8)

(-8, 0)

#74. Two angles are complementary. The larger angle is 3 times the smaller angle. What is the measure of the larger angle?

67.5°

30°

45°

22.5°

#75. Parallelogram interior angles: 3x and 2x + 50. Find x.

38

44

32

26

#76. Right triangle legs 11 m, 60 m. Hypotenuse?

61 m

71 m

49 m

55.5 m

#77. Distance (-2, 3) to (4, -5)?

10

8

6

12

#78. Midpoint (0, 5), (10, -5)?

(0, 0)

(10, 0)

(5, 0)

(5, 5)

#79. Adjacent sides of rectangle in ratio 3:5. Perimeter 64. Sides are?

15, 17

12, 20

8, 24

10, 22

#80. Vertical through (3, -5). Equation?

x = 3

y = -5

y = 3

x = -5

#81. Line (5, 7), (8, 13). Slope?

2

6

-2

1/2

#82. An equilateral triangle has each side measuring 13 meters. What is its perimeter?

169 m

39 m

52 m

26 m

#83. (0, 5) rotate 180°, origin. New?

(0, -5)

(-5, 0)

(0, 5)

(5, 0)

#84. Slope (0, 0), (5, 15)?

1/3

3

20

15

#85. (7, -3) translate . New?

(5, -11)

(9, -11)

(9, 5)

(5, 5)

#86. A circular fountain has a radius of 5.5 meters. What is its diameter?

11 m

2.75 m

5.5 m

30.25 m

#87. Distance (1, 1) to (4, 5)?

3

7

5

8

#88. Circle with inscribed square. Square side 10 cm. Circle radius?

5√2 cm

10√2 cm

10 cm

5 cm

#89. Slope (6, 8), (2, 0)?

-2

1/2

2

-1/2

#90. Translate (3, 5) 4 right, 2 down. New?

(7, 7)

(7, 3)

(1, 3)

(-1, 7)

#91. Right triangle, one leg 9, hypotenuse 15. Other leg?

24

12

6

3√21

#92. (5, 2) translate . Where?

(2, 7)

(8, 7)

(8, -3)

(2, -3)

#93. Sphere radius 6 inches. Volume? (V = 4/3 πr³, π ≈ 3.14)

904.32 in³

288 in³

113.04 in³

2419.2 in³

#94. Segment (10, 10), (2, 2). Midpoint?

(4, 4)

(8, 8)

(6, 6)

(12, 12)

#95. An isosceles triangle has vertex angle 52°. Each base angle is what?

26°

52°

64°

128°

#96. Inscribed angle 35°. Central angle of same arc?

35°

17.5°

70°

145°

#97. Composite: rectangle 10 × 6, triangle base 10, height 4. Total area?

20 sq units

80 sq units

100 sq units

60 sq units

#98. Rectangular box 15 × 10 × 8 m. Volume?

240 m³

2400 m³

600 m³

1200 m³

#99. Points (10, 5), (0, 0). Slope?

-2

-1/2

2

1/2

#100. Regular hexagon side 5 m. Area? (A = 3√3/2 × s², √3 ≈ 1.73)

150 m²

129.75 m²

43.25 m²

64.875 m²

#101. 30-60-90 triangle shorter leg 4. Hypotenuse?

12

8√3

4√3

8

#102. At a football stadium, three sight lines from a point create angles of 19°, 46°, and a third angle that completes 180°. What is the third angle?

145°

115°

25°

135°

#103. Line (1, 1), (4, 4). Slope?

1

1/3

-1

3

#104. Equilateral triangle side 17 cm. Perimeter?

51 cm

289 cm

34 cm

68 cm

#105. Two angles form a linear pair. One angle is 15° less than twice the other. If the smaller angle is x°, and they sum to 180°, what is x?

35

45

55

65

#106. (-3, -2) reflect y-axis. New?

(3, 2)

(-2, -3)

(-3, 2)

(3, -2)

#107. Circle dilate scale 2: circumference becomes what times?

4

√2

8

2

#108. (6, 2) rotate 180°, origin. New?

(6, 2)

(-2, -6)

(2, 6)

(-6, -2)

#109. Distance (10, 0) to (0, 10)?

10

5√2

20

10√2

#110. Circumference 62.8 cm. Radius? (C = 2πr, π ≈ 3.14)

31.4 cm

5 cm

10 cm

20 cm

#111. Reflect (2, -4) over y-axis. New?

(2, 4)

(4, 2)

(-2, 4)

(-2, -4)

#112. Perpendicular to y = 2x + 1. Slope?

-1/2

1/2

2

-2

#113. (6, -2) move 3 left, 5 up. Where?

(9, -7)

(9, 3)

(3, 3)

(3, -7)

#114. Slope 3x – y = 6? Rearranged to y = mx + b?

1/3

3

6

-3

#115. Buildings 60 m apart, heights 80 m, 20 m. Rooftop distance?

64.03 m

67.08 m

70 m

100 m

#116. Triangle sides are in ratio 3:4:5. Smallest side is 9. What is the perimeter?

27

36

45

60

#117. Equilateral triangle lines of symmetry?

1

0

2

3

#118. Regular octagon lines of symmetry?

1

4

2

8

#119. Two arcs with central angles 45° and 73°. Third arc angle?

208°

137°

242°

118°

#120. Triangle base 16 cm, height 11 cm. Area?

88 cm²

176 cm²

44 cm²

27 cm²

#121. Slope -1/2, y-intercept 4. Equation?

y = 2x + 4

y = -0.5x – 4

y = -0.5x + 4

y = 0.5x + 4

#122. Rotate (7, 0) 270° counterclockwise, origin. New?

(-7, 0)

(7, 0)

(0, -7)

(0, 7)

#123. y = -3x + 9. Slope and intercept?

9 slope, -3 intercept

-3 slope, -9 intercept

3 slope, -9 intercept

-3 slope, 9 intercept

#124. Circle diameter 26 inches. Circumference? (C = πd, π ≈ 3.14)

40.82 in

81.64 in

530.66 in

169 in

#125. (1, 8) rotate 180°. New?

(-1, 8)

(1, -8)

(-1, -8)

(8, 1)

#126. Diagonal of rectangle 20, one side 12. Other?

16

32

8

23.3

#127. Rectangle perimeter 56 cm. One side 18 cm. Other?

38 cm

10 cm

20 cm

38 cm

#128. Vertex (4, 7) reflect over y-axis. New?

(7, 4)

(-4, -7)

(4, -7)

(-4, 7)

#129. (-5, 2) rotate 180°. New?

(5, -2)

(2, -5)

(-2, 5)

(-5, 2)

#130. (0, 0) reflect y = x. New?

(0, 0)

#131. A(2, 3) translate . New A?

(-3, -1)

(-3, 7)

(7, -1)

(7, 7)

#132. A trapezoid has one pair of parallel sides measuring 16 cm and 22 cm. What is the length of the midsegment?

38 cm

19 cm

27 cm

6 cm

#133. Cylindrical tank radius 3 m, height 10 m. Volume? (V = πr²h, π ≈ 3.14)

282.6 m³

141.3 m³

565.2 m³

94.2 m³

#134. Triangular prism: equilateral triangle base side 6 cm, height 12 cm. Volume?

374.1 cm³

216 cm³

108 cm³

187.06 cm³

#135. In triangle ABC, angle A = 45°, angle B = 63°. What is angle C?

27°

108°

99°

72°

#136. In a triangle, one angle is twice another. The third is 30° more than the smallest. All angles sum to 180°. Find the angles.

45°, 90°, 45°

30°, 60°, 90°

40°, 80°, 60°

35°, 70°, 75°

#137. Triangular prism: base area 20 cm², length 8 cm. Volume?

160 cm³

80 cm³

320 cm³

28 cm³

#138. An isosceles triangle has a vertex angle of 48°. What is the measure of each base angle?

66°

84°

48°

132°

#139. A triangular garden has angles measuring 52°, 71°, and x°. What is the measure of x?

109°

67°

57°

123°

#140. x-intercept at 6, y-intercept at 3. Equation?

y = -0.5x + 3

y = 2x + 3

y = 6x + 3

y = 0.5x + 3

#141. (6, -2) rotate 270° counterclockwise. New?

(-2, -6)

(2, 6)

(2, -6)

(-2, 6)

#142. A chord in a circle has length 18 cm and is 5 cm from center. Radius?

√106 cm

14 cm

13 cm

23 cm

#143. Circle area 314 cm². Diameter? (A = πr², π ≈ 3.14)

20 cm

10 cm

31.4 cm

40 cm

#144. Endpoints (0, 6), (8, 0). Midpoint?

(4, 3)

(2, 4)

(8, 6)

(0, 0)

#145. Distance (9, 12) to (0, 0)?

12

9

15

21

#146. At an intersection, two streets form intersecting lines. If one angle is 68°, what is the vertically opposite angle?

68°

136°

112°

34°

#147. Scalene triangle lines of symmetry?

2

3

0

1

#148. Regular octagon, all sides 4.5 cm. Perimeter?

36 cm

20.25 cm

18 cm

9 cm

#149. Passes (2, 5) with m = 1/2. Equation?

y = 2x + 5

y = 0.5x – 4

y = 0.5x + 5

y = 0.5x + 4

#150. Distance (2, 8) to (2, 2)?

4

6

10

8

#151. Cylinder radius 2.5 m, height 8 m. Volume? (V = πr²h, π ≈ 3.14)

314 m³

31.4 m³

157 m³

78.5 m³

#152. Triangle (1, 1), (4, 1), (3, 3). Translate 2 right, 3 up. One new vertex?

(6, 4)

(5, 6)

(3, 4)

(1, 4)

#153. Triangle sides 11, 13, 8 cm. Perimeter?

44 cm

32 cm

52 cm

22 cm

#154. (2, 5) dilate scale 1/2, origin. New?

(4, 10)

(2, 5)

(1, 2.5)

(0.5, 1.25)

#155. Rectangle with sides a and b: perimeter 40, one side is 15. Other side?

10

25

5

8

#156. Corner (10, 8) translate . New?

(6, 2)

(6, 14)

(14, 2)

(14, 14)

#157. Ladder 15 m against wall, base 9 m out. Wall height?

18 m

24 m

6 m

12 m

#158. Central angle 144°. Inscribed angle subtending same arc?

144°

36°

288°

72°

#159. An obtuse triangle has angles 118°, 35°, and x°. What is x?

83°

63°

27°

153°

#160. Rectangular prism 10 ft × 6 ft × 4 ft. Volume?

480 ft³

20 ft³

240 ft³

120 ft³

#161. A parallelogram has angles of 62° and x°. If consecutive angles are supplementary, find x.

118°

31°

152°

62°

#162. Cone base radius 7 cm, height 24 cm. Volume? (V = 1/3 πr²h, π ≈ 3.14)

2464 cm³

1232 cm³

4071.04 cm³

616 cm³

#163. Horizontal line slope?

0

undefined

1

-1

#164. Two adjacent angles form a linear pair. One angle measures 127°. What is the measure of the other angle?

53°

127°

73°

234°

#165. (7, 3) reflect y = x. New?

(7, 3)

(3, 7)

(-7, -3)

(-3, -7)

#166. Center (-6, -2) to (10, 8)?

(-8, 5)

(16, 10)

(0, 0)

(2, 3)

#167. Square lines of symmetry?

2

4

0

1

#168. Tangent from external point and secant: external segment 8 cm, whole secant 20 cm. Tangent length?

14 cm

10 cm

12 cm

16 cm

#169. Through (1, 3), (3, 7). Equation?

y = 2x – 1

y = x + 2

y = 2x + 3

y = 2x + 1

#170. Rectangular frame 3 ft × 5 ft. Perimeter?

8 ft

16 ft

15 ft

30 ft

#171. Slope (-3, 1), (3, -5)?

1

2

-1

-2

#172. Through (0, 4), (3, 10). Equation?

y = 2x + 4

y = 2x – 4

y = x + 4

y = 3x + 4

#173. Slope (6, 2), (3, 8)?

2

-1/3

-2

3

#174. By the HL theorem, two right triangles are congruent. Triangle 1 has hypotenuse 17. Triangle 2 is congruent; what is its hypotenuse?

8.5

17

9

34

#175. Corner (-2, -4) translate 7 right, 6 up. New?

(-9, -10)

(-5, -2)

(5, 2)

(5, -4)

#176. An architect designs a roofline where two complementary angles meet. If one angle is 28°, what is the other angle?

56°

152°

72°

62°

#177. Ladder 13 m, base 5 m from wall. Height reached?

9 m

8 m

15.6 m

12 m

#178. Circle radius 13, chord at distance 5 from center. Chord length?

24

12

26

18

#179. Rotate (3, 4) 90° counterclockwise, origin. New?

(3, -4)

(4, 3)

(-4, 3)

(-3, 4)

#180. (0, 5) reflect x-axis. New?

(0, -5)

(0, 5)

(-5, 0)

(5, 0)

#181. Midpoint (-10, -6) to (4, 12)?

(-3, 3)

(7, 9)

(2, 3)

(-6, 6)

#182. Translate (2, -3) by . New?

(3, -1)

(-7, -7)

(-3, 1)

(7, 1)

#183. (6, -3) reflect x-axis. New?

(6, 3)

(-6, -3)

(-6, 3)

(-3, 6)

#184. y-intercept y = -2x + 7?

-2

14

7

0

#185. Distance from (0,0) to (3,4) on coordinate plane?

12

5

1

7

#186. Parallelogram base 17 inches, height 9 inches. Area?

76.5 in²

153 in²

306 in²

26 in²

#187. (4, 4) translate . New?

(3, 3)

(3, 5)

(5, 3)

(5, 5)

#188. (5, 8) reflect y = x. New?

(-8, -5)

(5, 8)

(8, 5)

(-5, -8)

#189. Distance (3, 7) to (6, 11)?

√34

4

5

√16

#190. Scalene triangle sides 6, 9, 12. It’s what type?

Right

Equilateral

Acute

Obtuse

#191. A triangle has one angle of 90°, another of 37°. What is the third angle?

127°

53°

47°

83°

#192. Dilate (5, 15) scale 2/5. New?

(2, 6)

(5, 15)

(1, 3)

(10, 30)

#193. (2, 9) reflect x-axis. New?

(2, -9)

(-2, -9)

(-2, 9)

(9, 2)

#194. Pyramid square base 9 m, height 12 m. Volume?

324 m³

432 m³

648 m³

1296 m³

#195. Sphere diameter 10 cm. Volume? (V = 4/3 πr³, π ≈ 3.14)

523.33 cm³

314 cm³

1046.66 cm³

261.67 cm³

#196. Slope (2, 5), (6, 5)?

undefined

-1

1

0

#197. (-4, -6) reflect x-axis. New?

(4, 6)

(-4, 6)

(4, -6)

(6, 4)

#198. Rhombus perimeter 44 cm. Each side?

11 cm

4 cm

44 cm

22 cm

#199. x-intercept y = 4x – 12?

3

-3

12

-12

#200. Slope (-2, 3), (2, 11)?

4

1/2

-1

2

#201. Trapezoid bases 8, 14 units, height 6 units. Area?

132 sq units

84 sq units

44 sq units

66 sq units

#202. Equilateral triangle side 10 cm. Altitude? (alt = √3/2 × side, √3 ≈ 1.73)

5 cm

17.3 cm

8.65 cm

10 cm

#203. Midpoint (0, 0), (8, 6)?

(2, 3)

(4, 3)

(0, 0)

(8, 6)

#204. Slope (4, 3), (7, 9)?

-2

2

3

1/2

#205. Half-sphere radius 6 cm. Volume? (V = 2/3 πr³, π ≈ 3.14)

904.32 cm³

226.08 cm³

452.16 cm³

113.04 cm³

#206. Square diagonal 10 cm. Side? (diagonal = side√2)

14.14 cm

20 cm

5 cm

7.07 cm

#207. Segment endpoints (-2, 4), (4, -2). Midpoint?

(1, 1)

(3, 1)

(0, 2)

(2, 2)

#208. (5, 0) reflect y-axis. New?

(-5, 0)

(0, 5)

(5, 0)

(0, -5)

#209. (1, 4) reflect y-axis. New?

(-1, -4)

(1, -4)

(-1, 4)

(4, 1)

#210. Circular garden radius 8 m. Segment area with chord 4 m from center?

12.3 m²

34.5 m²

67.0 m²

201.1 m²

#211. Triangle with sides 5, 5, and 8: is it acute, right, or obtuse?

Acute

Cannot determine

Obtuse

Right

#212. Square side 9 cm. Area?

81 cm²

18 cm²

36 cm²

729 cm²

#213. Distance (-5, -1) to (3, 5)?

14

8

12

10

#214. Dilate (4, 6) scale 2, origin. New?

(4, 6)

(2, 3)

(8, 12)

(12, 18)

#215. Cylinder diameter 8 inches, height 15 inches. Volume? (V = πr²h, π ≈ 3.14)

753.6 in³

1884 in³

376.8 in³

120 in³

#216. Distance P(-3, 4), Q(5, 1)?

√73

√26

5

8

#217. Slope 3, through (2, 5). y = mx + b?

y = 3x + 11

y = 3x – 1

y = -3x + 5

y = 3x + 1

#218. Slope 1/2, y-intercept 3. Equation?

y = 2x + 3

y = (1/2)x – 3

y = (1/2)x + 3

y = 3x + 1/2

#219. (2, 6) rotate 90° clockwise, origin. New?

(-2, 6)

(2, -6)

(-6, 2)

(6, -2)

#220. Right triangle AC = 9 cm, BC = 40 cm. AB?

31 cm

41 cm

49 cm

49.9 cm

#221. Parallelogram with base 13 m and slant side 10 m (perpendicular height 8 m). Area?

130 m²

80 m²

104 m²

65 m²

#222. Dilate (6, 8) scale 2/3. New?

(2, 8/3)

(9, 12)

(4, 16/3)

(6, 8)

#223. Two secants from external point: one external segment 6 cm, whole length 14 cm. Other whole length 16 cm, external segment?

8 cm

7.5 cm

10 cm

5.25 cm

#224. Circle radius 6 m. Area? (A = πr², π ≈ 3.14)

37.68 m²

56.52 m²

18.84 m²

113.04 m²

#225. Rectangular parking lot 85 m × 42 m. Perimeter?

127 m

254 m

3570 m

170 m

#226. Slope (-1, -2), (3, 6)?

4

1/2

-2

2

#227. In a geometric proof, angle A and angle B are supplementary. If angle A = (4x + 12)° and angle B = (8x – 48)°, find x.

12

15

10

20

#228. Slope (1, 4), (5, 12)?

-2

3

1/2

2

#229. Kite with one diagonal 18, other 24. Area?

216 sq units

432 sq units

54 sq units

108 sq units

#230. Vertical angles at an intersection: one angle is (7x – 8)° and the opposite is (5x + 12)°. Find x.

20

15

8

10

#231. Midpoint (6, 6), (0, 0)?

(3, 3)

(2, 2)

(0, 0)

(6, 6)

#232. Two points (4, 2), (2, 8). Center?

(4, 5)

(3, 5)

(6, 10)

(2, 3)

#233. Points (-5, -5), (5, 5). Slope?

-1

0

1

2

#234. Line passing (1, 2) translate . New point on line?

(0, 1)

(1, 2)

(4, 3)

(2, 4)

#235. Distance (-1, -1) to (2, 3)?

8

3

√41

5

#236. Trapezoid with bases in ratio 2:3. Perimeter including legs 40. If bases total 20, legs total?

25

10

15

20

#237. (6, 2) reflect over y = x. New?

(-2, -6)

(2, 6)

(6, 2)

(-6, -2)

#238. Rotate (5, 0) 180°, origin. New?

(-5, 0)

(0, 5)

(0, -5)

(5, 0)

#239. Distance (0, 0) to (8, 15)?

8

15

17

23

#240. Through (0, 0), (4, 8). Equation?

y = x + 4

y = 2x + 4

y = 4x

y = 2x

#241. Circle radius 7 cm. Tangent from point 25 cm away. Tangent length?

18 cm

24 cm

√576 cm

32 cm

#242. Quadrilateral sides 9, 12, 15, 8 m. Perimeter?

44 m

54 m

1296 m

34 m

#243. Pentagon regular side 7 m. Area? (≈ 84.3 m²)

50 m²

84.3 m²

42.15 m²

49 m²

#244. In a rectangle, one side is 12 inches and the other is 9 inches. What is the perimeter?

21 in

42 in

108 in

38 in

#245. Circular track circumference 400 m. Radius? (C = 2πr, π ≈ 3.14)

200 m

64 m

127.4 m

63.7 m

#246. Reflect (3, 5) over x-axis. New?

(3, -5)

(-3, 5)

(5, 3)

(-3, -5)

#247. (0, 0) translate . New?

(6, -4)

(-6, -4)

(-6, 4)

(6, 4)

#248. A rhombus has diagonals of length 18 cm and 24 cm. What is its area?

432 cm²

42 cm²

108 cm²

216 cm²

#249. Points A(1, 2), B(7, 10). Distance AB?

14

8

6

10

#250. 45-45-90 triangle hypotenuse 10. Leg?

5√2

5

7.07

10√2

Geometric and Spatial Reasoning – Set 2

Results

#1. (4, 4) reflect y-axis. New?

#2. Rectangle 24 m × 7 m. Diagonal?

#3. Chord 24 cm in circle radius 13 cm. Distance from center to chord?

#4. Cylinder radius 4 m, height 6 m. Volume? (V = πr²h, π ≈ 3.14)

#5. Rotate (-1, 2) 180°, origin. New?

#6. Cone diameter 12 cm, height 10 cm. Volume? (V = 1/3 πr²h, π ≈ 3.14)

#7. Two similar triangles have sides in ratio 2:3. Smaller has perimeter 20. Larger’s perimeter?

#8. Isosceles right triangle legs 6 cm. Hypotenuse?

#9. Cities (12, 18), (15, 22) on map. Distance?

#10. Square with area 49 sq cm. Perimeter?

#11. Rectangle 24 ft × 16 ft. Perimeter?

#12. Dilate (9, 12) scale 1/3, origin. New?

#13. Isosceles triangle lines of symmetry?

#14. Trapezoid lines of symmetry?

#15. Horizontal through (5, 7). Equation?

#16. In a 30-60-90 triangle, the shorter leg is 5. Hypotenuse is?

#17. Vertical angles: one is (2x + 24)°, the other is (5x – 9)°. Find x.

#18. Isosceles trapezoid bases 28 m, 18 m, legs 11 m each. Perimeter?

#19. Cone radius 3 m, height 9 m. Volume? (V = 1/3 πr²h, π ≈ 3.14)

#20. Vertical angles are formed by two intersecting lines. If one vertical angle measures 42°, what is the measure of the angle adjacent to it?

#21. Distance (0, 5) to (12, 0)?

#22. Square perimeter 52 cm. Side?

#23. (5, 5) move 2 right, 2 right. New?

#24. Rectangular prism 12 cm × 8 cm × 5 cm. Volume?

#25. An isosceles trapezoid has legs of 7 in and parallel bases of 9 in and 15 in. What is the perimeter?

#26. Corner (3, 8) translate 4 up, 1 down. New?

#27. Dilate (10, -8) scale 0.5, origin. New?

#28. Cone radius 5 cm, height 12 cm. Volume? (V = 1/3 πr²h, π ≈ 3.14)

#29. Shape corner (8, 5) move 2 left, 4 up. New?

#30. Endpoints (5, 1), (1, 5). Midpoint?

#31. Rotate (2, 3) 90° clockwise. New?

#32. (-8, 2) reflect y = x. New?

#33. Translate (1, 1) by . New?

#34. Two concentric circles: radii 6 and 3 cm. Annulus area? (A = π(R² – r²), π ≈ 3.14)

#35. Circular flower bed radius 3.5 m. Edging needed? (C = 2πr, π ≈ 3.14)

#36. Congruent triangles by SAS: two sides 12 and 18 with included angle 60°. Perimeter 50. Sides are?

#37. A kite has two pairs of adjacent equal sides: 6 cm, 6 cm, 11 cm, 11 cm. Perimeter?

#38. Midpoint (2, 8) to (6, 14)?

#39. Arc length 15.7 cm with radius 5 cm. Central angle? (arc = θ/360° × 2πr, π ≈ 3.14)

#40. Two points (6,8) and origin. Distance?

#41. In a right triangle, the acute angles measure 31° and x°. Find x.

#42. Distance (-6, 0) to (0, 8)?

#43. Pentagon regular, side 6 inches. Perimeter?

#44. Reflect (-1, 3) over x-axis. New?

#45. Two triangles satisfy the ASA congruence criterion. Triangle ABC has angles 52° and 63° with included side 14 cm. What is a corresponding angle in Triangle DEF?

#46. Four angles meet at a point around a circle, totaling 360°. Three angles measure 85°, 92°, and 73°. What is the fourth?

#47. y-intercept 2x + 5y = 10?

#48. A carpenter finds that two supplementary angles measure (3x + 15)° and (2x – 5)°. What is the value of x?

#49. Rhombus diagonals 14 cm, 20 cm. Area?

#50. A right isosceles triangle has legs of 8 inches. What is its perimeter?

#51. Rectangle sides 9 and 12. Diagonal?

#52. (0, 4) rotate 90° clockwise. New?

#53. Regular hexagon side 12 cm. Perimeter?

#54. Semicircle radius 8 m. Perimeter? (includes diameter)

#55. Slope through (1, 2), (4, 8)?

#56. Semicircle radius 9 inches. Area? (A = πr²/2, π ≈ 3.14)

#57. Endpoints (0, 0), (12, 8). Midpoint?

#58. Point (-1, 3) translate 5 right, 0 up. New?

#59. Distance (2, 2) to (5, 6)?

#60. Triangular sail base 8 m, height 6 m. Area?

#61. Vertical line slope?

#62. Two supplementary angles have a ratio of 3:7. What is the measure of the larger angle?

#63. Trapezoid bases 15 cm, 23 cm, height 8 cm. Area?

#64. Segment (-1, 5), (3, 1). Midpoint?

#65. Points (0, 3), (2, 7). Slope?

#66. Rectangle corner (0, 0), translate 6 left, 3 up. New?

#67. Rotate (3, 0) 90° clockwise. New?

#68. Triangular playground 27 m, 35 m, 19 m sides. Perimeter?

#69. Dilation scale 3: area becomes how many times larger?

#70. Rotate (-3, 5) 90° counterclockwise. New?

#71. (0, 0) translate . New?

#72. Points (8, 2), (3, 2). Slope?

#73. Rotate (0, -8) 90° counterclockwise, origin. New?

#74. Two angles are complementary. The larger angle is 3 times the smaller angle. What is the measure of the larger angle?

#75. Parallelogram interior angles: 3x and 2x + 50. Find x.

#76. Right triangle legs 11 m, 60 m. Hypotenuse?

#77. Distance (-2, 3) to (4, -5)?

#78. Midpoint (0, 5), (10, -5)?