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

Neither

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

`gradient \: of \: first \: line \\ = (1 - ( - 2))/(3 - ( - 2)) \\ = (1 + 2)/(3 + 2) \\ = (3)/(5)`

`gradient \: of \: the \: other \: line \\ = (5 - ( - 6))/(5 - 4) \\ = (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.