Question

line DE contains the points D(-1,-4) and E (3,3). Line FG contains the point F (-3,3).Which set of coordinates for point G makes the two lines perpendicular

Answer 1

The answer would be (-3,-7)

Answer 2

The set of coordinates for point G makes the two lines perpendicular is (4, 7)

How to determine the set of coordinates that makes the lines perpendicular

From the question, we have the following parameters that can be used in our computation:

D(-1,-4) and E (3,3).

Calculate the slope of DE using

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

So, we have

`m_(DE) = (3 + 4)/(3 + 1)`

`m_(DE) = (7)/(4)`

The slope of perpendicular lines are opposite reciprocals

This means that the slope of the line FG is

`m_(FG) = -(1)/(m_(DE))`

This gives

`m_(FG) = -(4)/(7)`

Using the slope formula and F = (-3, 3), we have

`m_(FG) = (3 - y)/(-3 - x)`

`(3 - y)/(-3 - x) = -(4)/(7)`

By comparison. we have

3 - y = -4

-3 - x = 7

Solving for x and y, we have

y = 3 + 4

x = -3 + 7

Evaluate

y = 7

x = 4

This means that

G = (4, 7)

Hence, the set of coordinates is (4, 7)