Question

What is the slope of any line perpendicular to the line passing through `(2,-22)` and `(18,-4)`?

Answer 1

Any line perpendicular to the line passing through these two points will have a slope of `-8/9`

Explanation:

First, we need to find the slope of the line passing through the two points in the problem. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(-4) - color(blue)(-22))/(color(red)(18) - color(blue)(2)) = (color(red)(-4) + color(blue)(22))/(color(red)(18) - color(blue)(2)) = 18/16 = 9/8`

The slope of the line passing through the two points is `m = 9/8`

A line perpendicular to this line will have a slope (let's call it `m_p`) will have a slope which is the negative inverse of the slope of this line or:

`m_p = -1/m`

Or, `m_p = -8/9`