Question

4.. Please help. Is DE←→ perpendicular to FG←→? Why or why not?

Answer 1

Given:

DE contains the points D(1, -2) and E(3, 4).

FG contains the points F(-1, 2) and G(4, 0).

To find:

Is DE perpendicular to FG.

Solution:

Slope of DE:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here $x_1=1, y_1=-2, x_2=3, y_2=4$

$m=\frac{4-(-2)}{3-1}$

$m=\frac{6}{2}$

m = 3

Slope of FG:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here $x_1=-1, y_1=2, x_2=4, y_2=0$

$m=\frac{0-2}{4-(-1)}$

$m=\frac{-2}{4+1}$

$m=\frac{-2}{5}$

Two lines are perpendicular if product their slopes are -1.

Slope of DE × Slope of FG

         $=3\times \frac{-2}{5}$

         $= \frac{-6}{5}$

         ≠ -1

The solution is no, because the product of the slopes is not -1.

Answer 2

Answer:

The second option:  no, because the product of the slopes is not -1.