Question

Question number.

11: A rectangle has its
vertices at (-2, 2), (-2,4)
and (3, 2). Give the
coordinate
vertex.

Answer 1

A rectangle has four vertices located on a coordinate plane. Three of the vertices are (-2, 1), (3, 1), and (3, -2). What is the area of the rectangle?

Forgetting for a second that it’s half a rectangle, in general the signed area of the triangle Δ

with vertices (a,b),(c,d),(e,f)

satisfies

2Δ=ad−bc+cf−de+eb−fa

2Δ=(−2)(1)−(1)(3)+3(−2)−1(3)+3(1)−(−2)(−2)=−15

The negative number means we went around clockwise; it doesn’t matter. In general 2Δ

is the signed area of any of three parallelograms implied by the three points. A right triangle is half a rectangle, so that rectangle’s area must be 2Δ.