Question

Given rectangle ABCD with vertices A(1, 4), B(3, 6), C(6, 3), and D(4, 1), what is the

perimeter of ABCD? Leave your answer in simplified radical form.

Answer 1

10√2

Explanation:

A(1, 4), B(3, 6), C(6, 3), D(4, 1)

The distance formula tells you the distance d between two points (x1, y1) and (x2, y2) is given by ...

d = √((x2-x1)² +(y2-y1)²

Then the side lengths are ...

AB = √(2² +2²) = √8 = 2√2

BC = √(3² +(-3)²) = √18 = 3√2

The perimeter is twice the sum of these sides, so is ...

P = 2(2√2 +3√2) = 10√2 . . . the perimeter of the rectangle