Question

(04.01 mc) which of the following best classifies a quadrilateral with coordinates a(2, 6), b(5, 1), c(10, 4), and d(7, 9)? rectangle parallelogram rhombus square

Explanation:

Step1: Calculate side lengths

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$AB=\sqrt{(5-2)^2+(1-6)^2}=\sqrt{9+25}=\sqrt{34}$
$BC=\sqrt{(10-5)^2+(4-1)^2}=\sqrt{25+9}=\sqrt{34}$
$CD=\sqrt{(7-10)^2+(9-4)^2}=\sqrt{9+25}=\sqrt{34}$
$DA=\sqrt{(2-7)^2+(6-9)^2}=\sqrt{25+9}=\sqrt{34}$

Step2: Calculate diagonal lengths

$AC=\sqrt{(10-2)^2+(4-6)^2}=\sqrt{64+4}=\sqrt{68}$
$BD=\sqrt{(7-5)^2+(9-1)^2}=\sqrt{4+64}=\sqrt{68}$

Step3: Check quadrilateral type

All sides equal, diagonals equal.

Answer:

D. Square