Question

Determine whether the lines are parallel or perpendicular or neither.

One lines passes through points (3, 1) and (−2, −2);
another line passes through points (5, 5) and (4, −6)

Answer 1

Answer:

Neither

Step-by-step explanation:

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

Let's find the gradient of each line first.

$\boxed{gradient = \frac{y1 - y2}{x1 - x2} }$

$gradient \: of \: first \: line \\ = \frac{1 - ( - 2)}{3 - ( - 2)} \\ = \frac{1 + 2}{3 + 2} \\ = \frac{3}{5}$

$gradient \: of \: the \: other \: line \\ = \frac{5 - ( - 6)}{5 - 4} \\ = \frac{5 + 6}{1} \\ = 11$

Product of the gradients

= 11 ×⅗

= 6.6

Since the gradients are neither the same, nor do the product of the gradients equal to -1, the 2 lines are neither parallel or perpendicular to each other.