Question

What is the slope of any line perpendicular to the line passing through `(15,-22)` and `(12,-15)`?

Answer 1

`m=3/7`

Explanation:

Given 2 perpendicular lines with slopes `m_1" and " m_2` then

`color(red)(bar(ul(|color(white)(a/a)color(black)(m_1xxm_2=-1)color(white)(a/a)|)))`

We require to calculate `m_1` using the `color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"`

The 2 points here are (15 ,-22) and (12 ,-15)

`rArrm_1=(-15-(-22))/(12-15)=7/(-3)=-7/3`

Thus `-7/3xxm_2=-1`

`rArrm_2=(-1)/(-7/3)=3/7`

Hence the slope of any line perpendicular to the line passing through the 2 given points is `m=3/7`