Question

Which term best describes the

quadrilateral formed by A(2, 3),
B(4, 6), C(8, 9), and D(5,5)?

Answer 1

A kite

Explanation:

The coordinates of the vertices of the quadrilateral are;

A(2, 3), B(4, 6), C(8, 9), and D(5, 5), therefore, the length of the sides of the quadrilateral can be found using the following formula;

`l = \sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

(x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints on the side

For side AB, we have;

`l_(AB) = \sqrt{\left (6 - 3 \right )^(2)+\left (4-2 \right )^(2)} = √(13)`

The slope = 1.5

For side BC, we have;

`l_(BC) = \sqrt{\left (9 - 6 \right )^(2)+\left (8-4 \right )^(2)} = 5`

The slope = 3/4

For side CD, we have;

`l_(CD) = \sqrt{\left (5 - 9 \right )^(2)+\left (5-8 \right )^(2)} = 5`

The slope = 4/3

For side DA, we have;

`l_(DA) = \sqrt{\left (3 - 5 \right )^(2)+\left (2-5 \right )^(2)} = √(13)`

The slope = 2/3

Angle ADC = Actan (2/3 - 4/3)/(1 + 2/3*4/3) = -19.44 = 180-19.44 = 160.55°

Angle ABC = Actan (0.75 - 1.5)/(1 + 0.75*1.5) = -19.44 = 180-19.44 = 160.55°

Therefore, given that the quadrilateral has two pairs of equal adjacent sides and the angles are equal at the meeting point of the two squares, it is best described as a kite.