CHSPE Geometry 4

Question 1

What is the midpoint of the segment with endpoints (2, 4) and (8, 10)?

Accepted Answer

(5, 7)

Answer

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)

Accepted Answer

9.42 cm

Answer

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?

Accepted Answer

70° each

Answer

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)?

Accepted Answer

2

Answer

Slope = (9 − 1) / (7 − 3) = 8 / 4 = 2.

Question 5

A square has a diagonal of length 10 cm. What is the side length?

Accepted Answer

5√2 cm

Answer

For a square with side s, diagonal = s√2, so s = 10 / √2 = 5√2 ≈ 7.07 cm.

California High School Proficiency Exam Practice Test