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

Answer:

Neither

Step-by-step explanation:

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

$Gradient= \frac{y1-y2}{x1-x2}$

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

Gradient of 1st line

$=\frac{4-(-4)}{-7-5} \\=\frac{4+4}{-12}\\ =-\frac{8}{12} \\=-\frac{2}{3}$

Gradient of the other line

$=\frac{2-(-4)}{2-(-7)} \\=\frac{2+4}{2+7}\\=\frac{6}{9} \\=\frac{2}{3}$

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

Product of the gradient

$=\frac{2}{3} (-\frac{2}{3})\\=-\frac{4}{9}$

≠ -1

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