Question

Plot the vertices (-2, -8), (-2, 2), and (8, 2).

What is the last vertex of the rectangle?
What is the area of the rectangle?
square units

Answer 1

the last vertex is (8,-8)

the area of the rectangle is 100 square units

Explanation:

Answer 2

• (8, -8)
• 100 square units

Explanation:

The diagonals of a rectangle have the same midpoint, so for points A, B, C, D, we must have ...

(A+C)/2 = (B+D)/2

D = A + C - B

D = (-2, -8) +(8, 2) -(-2, 2) = (-2+8+2, -8+2-2)

D = (8, -8)

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The side lengths are 2-(-8) = 10, and 8-(-2) = 10. The area is the product of the side lengths, so is 10×10 = 100 square units.

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Comment on side lengths

When the end points of one side are on the same vertical line, the length of that side is the difference of y-coordinates. When the points lie on the same horizontal line, the side length is the difference of x-coordinates.