Question

Which term best describes the quadrilateral formed by A(2, 3), B(4, 6), C(8, 9), and D(5,5)?

Answer 1

Answer:

A kite

Step-by-step 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;

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

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;

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

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.