Question

Are the lines parallel, perpendicular, or neither?

One line passes through the points (3, 2) and (6,8), and the other line passes through
the points (0, 2) and (2,6).
Is it neither parallel or perpendicular please help

Answer 1

Answer: The lines are parallel

Explanation:

In order to determine whether the lines are parallel (have the same gradient), perpendicular (gradients are negative reciprocal) or neither, we have to find the gradient of each line.

gradient = (y₂ - y₁) / (x₂ - x₁)

Let the line with points (3, 2) and (6, 8) = [a]

& (0, 2) and (2, 6) = [b]

Now, gradient of [b] = (6 - 2) / (2 - 0) = 2

gradient of [a] = (8 - 2) / (6 - 3) = 2

Since m of [a] = m of [b]

⇒ [a] ║ [b]