Question

Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle? a coordinate plane with quadrilateral ABCD at A negative 2 comma 0, B 0 comma negative 2, C negative 3 comma negative 5, D negative 5 comma negative 3 Prove that segments AD and AB are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are equal. Prove that segments BC and CD are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Answer 1

Answer:

Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step explanation:

In Quadrilateral ABCD with points A(-2,0), B(0,-2), C(-3,-5), D(-5,-3)

Using the distance formula

d =  sqrt(x2-x1)^2+(y2-y1)^2

|AB| = sqrt(0-(-2))^2+(-2-0)^2 = sqrt(8) = 2sqrt(2)

|CD| = sqrt(-5+3))^2+(-3+5)^2) = sqrt(8) = 2sqrt(2)

|BC| = sqrt(-3-0))^2+(-5+2)^2 = sqrt(18) = 3sqrt(2)

|AD| sqrt(-5+2)^2+(-3-0)^2 = sqrt(18) = 3sqrt(2)

Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.

Next, let us consider the slope.

Slope of |AB| = _-2-0_______ =__-2__  = -1

                          0-(-2)                     2

Slope of |BC| = __-5+2___ =    _-3___  =  1

                            -3-0                  -3

Since the slopes of consecutive sides are opposite reciprocals, therefore ABCD is a rectangle.