NJSLA Geometric Principles and Measurement 5 — Questions and Answers
Question 1: A right triangle has legs of length 7 cm and 24 cm. What is the length of the hypotenuse?
- 20 cm
- 25 cm (Correct answer)
- 28 cm
- 31 cm
Correct answer: 25 cm
c = √(7² + 24²) = √(49 + 576) = √625 = 25 cm.
Question 2: The area of a circle is 50.24 cm². What is its diameter? (Use π ≈ 3.14)
- 4 cm
- 6 cm
- 8 cm (Correct answer)
- 10 cm
Correct answer: 8 cm
r² = 50.24/3.14 = 16, so r = 4 cm and diameter = 8 cm.
Question 3: Two parallel lines are cut by a transversal. Which pair of angles is always equal?
- Co-interior angles
- Supplementary angles
- Alternate interior angles (Correct answer)
- Adjacent angles
Correct answer: Alternate interior angles
Alternate interior angles are congruent when two parallel lines are cut by a transversal.
Question 4: A figure is reflected over the y-axis. If a point was at (5, −3), where is its image?
- (−5, 3)
- (−5, −3) (Correct answer)
- (5, 3)
- (3, −5)
Correct answer: (−5, −3)
Reflection over the y-axis negates the x-coordinate: (5, −3) → (−5, −3).
Question 5: A triangular prism has a triangular base with base 6 cm and height 4 cm, and the prism's length is 10 cm. What is its volume?
- 60 cm³
- 120 cm³ (Correct answer)
- 240 cm³
- 180 cm³
Correct answer: 120 cm³
V = (area of triangle) × length = ½(6)(4) × 10 = 12 × 10 = 120 cm³.
Question 6: What is the measure of each interior angle of a regular octagon?
- 108°
- 120°
- 135° (Correct answer)
- 144°
Correct answer: 135°
Sum of interior angles = (8 − 2) × 180° = 1080°; each angle = 1080° ÷ 8 = 135°.
Question 7: A dilation centered at the origin with scale factor 3 maps point A(2, −4) to which image?
- (5, −7)
- (6, −12) (Correct answer)
- (2/3, −4/3)
- (−6, 12)
Correct answer: (6, −12)
Multiply each coordinate by the scale factor: (2 × 3, −4 × 3) = (6, −12).
NJSLA Geometric Principles and Measurement 5
A right triangle has legs of length 7 cm and 24 cm.
What is the length of the hypotenuse?