GRE Plane and Coordinate Geometry 3

Question 1

In a right triangle, the legs are 6 and 8. What is the hypotenuse?

Accepted Answer

10

Answer

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?

Accepted Answer

90°

Answer

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?

Accepted Answer

x² + y² = 16

Answer

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?

Accepted Answer

y = x + 1

Answer

Using y − 3 = 1(x − 2) gives y = x + 1.

Question 5

What is the circumference of a circle with diameter 10?

Accepted Answer

10π

Answer

Circumference = πd = π × 10 = 10π.

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