GRE - Graduate Record Examinations Plane and Coordinate Geometry Questions and Answers

Question 1

In the xy-plane, a triangle has vertices at A(1, 2), B(7, 2), and C(3, 8). What is the length of the median from vertex A to the side BC?

Accepted Answer

5

Answer

√41

Answer

6

Answer

√52

Question 2

Which of the following is an equation of a line that is perpendicular to the line 2x + 5y = 10 and passes through the point (4, 1)?

Accepted Answer

5x - 2y = 18

Answer

2x + 5y = 13

Answer

2x - 5y = 3

Answer

5x + 2y = 22

Question 3

What is the area of the quadrilateral with vertices at coordinates (-2, 1), (4, 1), (2, 5), and (0, 5) in the xy-plane?

Accepted Answer

16

Answer

20

Answer

24

Answer

32

Question 4

A circle in the xy-plane has its center at (-3, 5). If the point (1, 8) lies on the circle, what is the area of the circle?

Accepted Answer

25π

Answer

5π

Answer

10π

Answer

50π

Question 5

Point P has coordinates (a, b). Point Q is the reflection of point P across the line y = x. Point R is the reflection of point Q across the y-axis. What are the coordinates of point R?

Accepted Answer

(-b, a)

Answer

(b, -a)

Answer

(-a, b)

Answer

(a, -b)

Question 6

What is the area of the triangle formed in the first quadrant by the line with the equation 3x + 4y = 24 and the coordinate axes?

Accepted Answer

24

Answer

12

Answer

48

Answer

18