Question

A quadrilateral is graphed in the coordinate plane below. Which classification best describes the quadrilateral (parallelogram, rhombus, etc.)?

Answer 1

Answer:

Trapezoid

Step-by-step explanation:

Given quadrilateral has vertices at points A(-2,-1), B(3,13), C(15,5) and D(13,-11).

Find slopes of lines AD and BC:

$\text{Slope}_{AD}=\dfrac{y_D-y_A}{x_D-x_A}=\dfrac{-11-(-1)}{13-(-2)}=\dfrac{-11+1}{13+2}=\dfrac{-10}{15}=-\dfrac{2}{3}\\ \\\text{Slope}_{BC}=\dfrac{y_C-y_B}{x_C-x_B}=\dfrac{5-13}{15-3}=\dfrac{-8}{12}=-\dfrac{2}{3}$

Since the slopes are the same, lines AD and BC are parallel.

Find slopes of lines ABD and CD:

$\text{Slope}_{AB}=\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{13-(-1)}{3-(-2)}=\dfrac{14}{5}\\ \\\text{Slope}_{CD}=\dfrac{y_D-y_C}{x_D-x_C}=\dfrac{-11-5}{13-15}=\dfrac{-16}{-2}=8$

Since the slopes are different, lines AB and CD are not parallel.

This means quadrilateral ABCD is trapezoid (two opposite sides - parallel and two another opposite sides - not parallel)