Question

Ivan used coordinate geometry to prove that quadrilateral efgh is a square.

Answer 1

A square has parallel opposite sides, and congruent four sides.

The coordinates of the square are given as:

$E = (-2,3)$

$F=(1,6)$

$G =(4,3)$

$H = (1,0)$

Calculate the distance between the vertices of the square using the following distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_1)^2}$

So, we have:

$E F= \sqrt{(-2- 1)^2 + (3- 6)^2}$

$EF = \sqrt{18}$

$FG= \sqrt{(4- 1)^2 + (3- 6)^2}$

$FG= \sqrt{18}$

$GH = \sqrt{(4 -1)^2 + (3 - 0)^2}$

$GH = \sqrt{18}$

$HE = \sqrt{(1--2)^2 + (0 -3)^2}$

$HE = \sqrt{18}$

Notice that all the side lengths of the square are the same.

Hence, the quadrilateral EFGH is square

Read more about squares at:

brainly.com/question/25926201