Question

Tell one the lines for the given points are parallel, perpendicular, or neither. Just your answer.

Line 1: (2, -3), (-4, -6)
Line 2: (-3, 2), (2, -8)

Answer 1

Perpendicular

Explanation:

Given

`Line\ 1: (2, -3), (-4, -6)`

`Line\ 2: (-3, 2), (2, -8)`

Required

Tell the relationship between both lines

We start by calculating the slopes (m) of both lines.

`m = (y_2 - y_1)/(x_2 - x_1)`

For Line 1:

`m_1 = (-6 - (-3))/(-4 - 2)`

`m_1 = (-6 +3)/(-4 - 2)`

`m_1 = (-3)/(-6)`

`m_1 = (1)/(2)`

For Line 2:

`m_2 = (-8 - 2)/(2 - (-3))`

`m_2 = (-8 - 2)/(2 +3)`

`m_2 = (-10)/(5)`

`m_2 = -2`

The lines are not parallel because
`m_1 \\e m_2`

However, they are perpendicular, because:

`m_1 = -(1)/(m_2)`

To prove this, substitute values for m1 and m2

`(1)/(2) = -(1)/(-2)`

`(1)/(2) = (1)/(2)` --- Proved