We are given coordinates of A, B, C and D :
A(2, 4), B(9, 8), C(-1, 2), and D(3, -5).
Now, we need to find the slopes of AB and CD.
Slope of AB is :
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(2,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:8\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%282%2C%5C%3A4%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%289%2C%5C%3A8%5Cright%29)
![m=\frac{8-4}{9-2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B8-4%7D%7B9-2%7D)
.
Slope of CD is:
![m=\frac{-5-2}{3-\left(-1\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-5-2%7D%7B3-%5Cleft%28-1%5Cright%29%7D)
.
<em>Slope of CD is negative reciprocal of slope of slope of AB. </em>
<h3>Therefore, lines AB are CD are perpendicular.</h3>