Question

The midpoints of the four sides of a rectangle are $(-3, 0),$ $(2, 0),$ $(5, 4),$ and $(0, 4).$ What is the area of the rectangle?

$20$

$25$

$40$

$50$

$80$

Answer: C

Concepts:coordinate geometry parallelogram midpoint

Difficulty rating: 1310

Solution:

The four given midpoints form a parallelogram. Its horizontal base has length $2-(-3)=5$ , and its height is $4$ , so its area is $5\cdot4=20$ .

For any rectangle, the parallelogram formed by joining the side midpoints has half the area of the rectangle. Therefore the rectangle's area is $2\cdot20=40$ .

Thus, the correct answer is C.

2022 AMC 8 Problem 18

Answer: C

Difficulty rating: 1310

Solution:

Problem 18 in Other Years