Question

1) Quadrilateral PQRS has vertices P(-3,-4), Q(9,5), R(-1,10), and S(-5,7). Prove that quadrilateral PQRS is an isosceles trapezoid.

Answer 1

First, locate each coordinate point on a graph, and join the points with straight lines.

An iscosceles trapezoid has equal base angles and equal left and right sides.

Sides:

SP and RQ

Apply Pythagorean theorem to find the lengths.

C^2 = a^2 + b^2

SP^2 =2^2 + 11^2

SP^2 = 4 + 121

SP ^2= 125

SP =√125

SP = 5

RQ^2 = 5^2 +10^2

RQ^2 = 25 + 100

RQ^2 = 125

RQ = √125

RQ = 5

Since both left and right sides are equal it is an isosceles trapezoid.