Question

On your own paper, graph the coordinates of quadrilateral ABCD.

● A(-3, 0)
● B(2, 4)
● C(6, -1)
● D(1, -5)

A) Identify what type of quadrilateral ABCD will be and give an explanation of your response. You must also justify it algebraically by showing your work to support your response.

B) What is the perimeter and area of quadrilateral ABCD?

Answer 1

A) Square

B) Perimeter: 4sqrt(41) units

Area: 41 units²

Explanation:

AB and CD are parallel because both have the same gradient:

AB: (-3-2)/(0-4) = 5/4

CD: (6-1)/(-1--5) = 5/4

AD and BC are parallel because both have the same gradient:

AD: (-3-1)/(0--5) = -4/5

BC: (6-2)/(-1-4) = -4/5

Since (5/4) × (-4/5) = -1

All angles are 90 (Perpendicular)

Lengths

CD = AB = sqrt[(-3-2)²+(0-4)²] = sqrt(41)

BC = AD = sqrt[(6-2)²+(-1-4)²] = sqrt(41)

Therefore all sides are equal in length

Hence it's a square

Perimeter = 4s = 4sqrt(41) units

Area = s² = [sqrt(41)]² = 41 units²