Question

Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain your answer.

Answer 1

We are given a rectangle ABCD

A(-2, 3)

B(4, 6)

We are asked to find the slopes of sides BC, CD, and DA.

Let me first draw a rectangle to better understand the problem

Recall that the slope is given by

$m=\frac{y_2−y_1}{ x_2−x_1}$$\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)$

So the slope of side AB is

$m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5$

The sides BC and DA are perpenducluar to the side AB.

So their slopes will be

$m_{BC}=m_{DA}=\frac{1}{-m_{AB}}$

Substituting the value of slope of AB

$m_{BC}=m_{DA}=\frac{1}{-0.5}=-2$

The side CD is parallel to the side AB.

Parallel sides have equal slopes so

$m_{CD}=m_{AB}=\frac{1}{2}$

Therefore, the slopes of the rectangle ABCD are

$\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}$