GRE Plane and Coordinate Geometry 3 — Questions and Answers
Question 1: In a right triangle, the legs are 6 and 8. What is the hypotenuse?
- 10 (Correct answer)
- 14
- 12
- √14
Correct answer: 10
By the Pythagorean theorem, √(6² + 8²) = √100 = 10.
Question 2: The interior angles of a triangle are in the ratio 1:2:3. What is the largest angle?
- 90° (Correct answer)
- 60°
- 120°
- 30°
Correct answer: 90°
The parts total 6, so angles are 30°, 60°, 90°, the largest being 90°.
Question 3: What is the equation of a circle centered at the origin with radius 4?
- x² + y² = 16 (Correct answer)
- x² + y² = 4
- x² + y² = 8
- (x−4)² + y² = 4
Correct answer: x² + y² = 16
A circle at the origin is x² + y² = r², so x² + y² = 16.
Question 4: A line passes through (2, 3) with slope 1. What is its equation in slope-intercept form?
- y = x + 1 (Correct answer)
- y = x + 3
- y = x − 1
- y = 2x + 1
Correct answer: y = x + 1
Using y − 3 = 1(x − 2) gives y = x + 1.
Question 5: What is the circumference of a circle with diameter 10?
- 10π (Correct answer)
- 20π
- 5π
- 25π
Correct answer: 10π
Circumference = πd = π × 10 = 10π.
Question 6: A rectangle has length 12 and width 5. What is the length of its diagonal?
- 13 (Correct answer)
- 17
- √17
- 60
Correct answer: 13
Diagonal = √(12² + 5²) = √169 = 13.
Question 7: Point (a, b) lies in Quadrant II. What are the signs of a and b?
- a < 0, b > 0 (Correct answer)
- a > 0, b > 0
- a < 0, b < 0
- a > 0, b < 0
Correct answer: a < 0, b > 0
Quadrant II has negative x-values and positive y-values.
GRE Plane and Coordinate Geometry 3
In a right triangle, the legs are 6 and 8.
What is the hypotenuse?