GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry 2 — Questions and Answers
Question 1: Line L has equation y = 3x + 4. What is the slope of a line perpendicular to L?
- -1/3 (Correct answer)
- 3
- -3
- 1/3
Correct answer: -1/3
Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 3 is −1/3.
Question 2: What is the area of a triangle with base 10 and height 6?
- 30 (Correct answer)
- 60
- 15
- 20
Correct answer: 30
Area of a triangle = ½ × base × height = ½ × 10 × 6 = 30.
Question 3: A line passes through the origin and the point (3, 9). What is its equation?
- y = 3x (Correct answer)
- y = 9x
- y = x + 3
- y = 3x + 9
Correct answer: y = 3x
The slope is 9/3 = 3, and since it passes through the origin (b = 0), the equation is y = 3x.
Question 4: The circumference of a circle is 16Ï€. What is the area of the circle?
- 64Ï€ (Correct answer)
- 8Ï€
- 16Ï€
- 32Ï€
Correct answer: 64Ï€
Circumference 2πr = 16π gives r = 8; area = πr² = π(64) = 64π.
Question 5: An equilateral triangle has a side length of 6. What is its area?
- 9√3 (Correct answer)
- 18
- 12√3
- 36
Correct answer: 9√3
Area of an equilateral triangle = (s²√3)/4 = (36√3)/4 = 9√3.
Question 6: What is the y-intercept of the line 4x − 2y = 8?
- -4 (Correct answer)
- 4
- 2
- -2
Correct answer: -4
Rearranging: −2y = −4x + 8, so y = 2x − 4; the y-intercept is −4.
GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry 2
Line L has equation y = 3x + 4.
What is the slope of a line perpendicular to L?