Question

determine whether ab and cd are

1. a(3,6), b(3,0), c(-4,5), d(2,5)

Explanation:

Step1: Find slope of AB

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(3,6)$ and $B(3,0)$, $x_1 = 3,y_1 = 6,x_2 = 3,y_2 = 0$. Then $m_{AB}=\frac{0 - 6}{3 - 3}$, which is undefined since the denominator is 0. This means AB is a vertical line.

Step2: Find slope of CD

For points $C(-4,5)$ and $D(2,5)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $x_1=-4,y_1 = 5,x_2 = 2,y_2 = 5$. So $m_{CD}=\frac{5 - 5}{2-(-4)}=\frac{0}{6}=0$. This means CD is a horizontal line.

Step3: Determine relationship

A vertical line and a horizontal line are perpendicular. So AB and CD are perpendicular.

Answer:

AB and CD are perpendicular.