Question

What is the slope of any line perpendicular to the line passing through `(24,-2)` and `(18,19)`?

Answer 1

`m = 2/7`

Explanation:

The first step is to calculate the gradient (m) of the line joining the 2 points using the `color(blue)" gradient formula "`

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

where `(x_1,y_1) " and " (x_2,y_2) " are the coords of 2 points "`

let `(x_1,y_1) = (24,-2) " and " (x_2,y_2) = (18,19)`

substitute these values into formula for m.

`rArr m = (19+2)/(18-24) = 21/-6 = -7/2`

Now if 2 lines with gradients `m_1 " and m_2` are perpendicular

then their product `m_1 . m_2 = -1`

let `m_2 " be gradient of perpendicular line "`

`rArr m_2 = (-1)/m_1 = -1/(-7/2) = 2/7`