Question

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

Answer 1

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

Answer 2

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=(y_2-y_1)/(x_2-x_1)`

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

`$m=(4-(-2))/(3-1)`

`$m=(6)/(2)`

m = 3

Slope of FG:

`$m=(y_2-y_1)/(x_2-x_1)`

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

`$m=(0-2)/(4-(-1))`

`$m=(-2)/(4+1)`

`$m=(-2)/(5)`

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

Slope of DE × Slope of FG

`$=3* (-2)/(5)`

`$= (-6)/(5)`

≠ -1

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