4.09: Coordinate Proofs

Question

Four points determine a square on the coordinate plane. What if you only have two points? Could you find the other points?

Two vertices of a quadrilateral are A(−3,2)  and B(2,−1).

1. Identify the vertices of square ABCD with the given coordinates for A and B.
2. Prove that the figure with those four vertices is a rectangle.

Answer 1

points a -3,2

b 2,-1

c -1,-6

d -6,-3

ad -3-(-6)=3

bc 2-(-1)=3

ab -3-2=-5

dc -6-(-1)=-5

This is a square.