Question

Given the points A(4,6), B(6,10), C(0,13), and D(-2,9). Determine the type of quadrilateral by using coordinate geometry. Explain how you achieved your answer and show all work!

Answer 1

We were given the following points;

A(4,6), B(6,10), C(0,13) , D(-2,9).

Slope of AB = (10-6)/(6-4)

= 4/2

=2

Slope of CD = (13-9)/(0--2)

= 4/2

=2

Slope of AD = (9-6)/(-2-4)

= 3/-6

= -½

Slope of BC = (13-10)/(0-6)

= 3/-6

= - ½

Slope of AB = slope of DC= 2

This tells us that side AB and DC of the quadrilateral are parallel.

Also

Slope of AD = slope of BC= - ½

This tells us that side AD and BC of the quadrilateral are also parallel.

Again;

Slope of AB × AD = 2 × - ½ = -1

This tells us that AB is perpendicular to AD.

Similarly;

Slope of AB × BC = 2 × - ½ = -1

This tells us that AB is perpendicular to BC.

The same thing applies to BC and CD, CD an AD.

The quadrilateral is therefore a rectangle.