Question

1. use slope to determine if the object below is a parallelogram. if not, please explain why.

Explanation:

First, identify the 4 vertices of the quadrilateral from the graph: let's define them as $A(-4, 2)$, $B(-1, 0)$, $C(1, -4)$, $D(-2, -2)$.

Step1: Calculate slope of AB

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\text{Slope of } AB = \frac{0-2}{-1-(-4)} = \frac{-2}{3}$

Step2: Calculate slope of CD

$\text{Slope of } CD = \frac{-2-(-4)}{-2-1} = \frac{2}{-3} = -\frac{2}{3}$

Step3: Calculate slope of BC

$\text{Slope of } BC = \frac{-4-0}{1-(-1)} = \frac{-4}{2} = -2$

Step4: Calculate slope of DA

$\text{Slope of } DA = \frac{2-(-2)}{-4-(-2)} = \frac{4}{-2} = -2$

Step5: Compare slopes for parallelism

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (equal slopes). Here, $\text{Slope of } AB = \text{Slope of } CD$, and $\text{Slope of } BC = \text{Slope of } DA$.

Answer:

The object is a parallelogram, because both pairs of its opposite sides have equal slopes, meaning they are parallel.