Question

One line passes through the points (-7, 4) and (5,-4). Another line passes through points (-7, - 4) and

(2,2).
Are the lines parallel, perpendicular, or neither?

Answer 1

Neither

Explanation:

Let's find the gradients of the two lines first.

`Gradient= (y1-y2)/(x1-x2)`

Parallel lines have the same gradient and the product of the gradients of perpendicular lines is -1.

Gradient of 1st line

`=(4-(-4))/(-7-5) \\=(4+4)/(-12)\\ =-(8)/(12) \\=-(2)/(3)`

Gradient of the other line

`=(2-(-4))/(2-(-7)) \\=(2+4)/(2+7)\\=(6)/(9) \\=(2)/(3)`

Since the two gradients are not equal, the lines are not parallel to each other.

Product of the gradient

`=(2)/(3) (-(2)/(3))\\=-(4)/(9)`

≠ -1

Thus, the 2 lines are not perpendicular to each other.