GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry 2

Question 1

Line L has equation y = 3x + 4. What is the slope of a line perpendicular to L?

Accepted Answer

-1/3

Answer

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?

Accepted Answer

30

Answer

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?

Accepted Answer

y = 3x

Answer

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 16π. What is the area of the circle?

Accepted Answer

64π

Answer

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?

Accepted Answer

9√3

Answer

Area of an equilateral triangle = (s²√3)/4 = (36√3)/4 = 9√3.

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