CHSPE Geometry 4 — Questions and Answers
Question 1: What is the midpoint of the segment with endpoints (2, 4) and (8, 10)?
- (4, 6)
- (5, 7) (Correct answer)
- (6, 7)
- (3, 5)
Correct answer: (5, 7)
Midpoint = ((2+8)/2, (4+10)/2) = (5, 7).
Question 2: A sector of a circle has a central angle of 90° and a radius of 6 cm. What is the arc length? (Use π ≈ 3.14)
- 9.42 cm (Correct answer)
- 18.84 cm
- 4.71 cm
- 37.68 cm
Correct answer: 9.42 cm
Arc length = (90/360) × 2πr = 0.25 × 2 × 3.14 × 6 ≈ 9.42 cm.
Question 3: An isosceles triangle has a vertex angle of 40°. What are the base angles?
- 40° each
- 70° each (Correct answer)
- 65° each
- 80° each
Correct answer: 70° each
Base angles are equal; (180 − 40) / 2 = 70° each.
Question 4: What is the slope of a line passing through (3, 1) and (7, 9)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (9 − 1) / (7 − 3) = 8 / 4 = 2.
Question 5: A square has a diagonal of length 10 cm. What is the side length?
- 5 cm
- 5√2 cm (Correct answer)
- 10√2 cm
- 7.07 cm
Correct answer: 5√2 cm
For a square with side s, diagonal = s√2, so s = 10 / √2 = 5√2 ≈ 7.07 cm.
Question 6: What is the measure of each interior angle of a regular hexagon?
- 108°
- 120° (Correct answer)
- 135°
- 144°
Correct answer: 120°
Sum of interior angles = (6 − 2) × 180 = 720°; each angle = 720 / 6 = 120°.
Question 7: Two angles are complementary. One measures 32°. What does the other measure?
- 148°
- 68°
- 58° (Correct answer)
- 48°
Correct answer: 58°
Complementary angles sum to 90°, so the other angle = 90 − 32 = 58°.
CHSPE Geometry 4
What is the midpoint of the segment with endpoints (2, 4) and (8, 10)?