Question

What is the slope of any line perpendicular to the line passing through `(1,2)` and `(-8,1)`?

Answer 1

`-9`

Explanation:

The slope of any line perpendicular to line passing through the points `(1, 2)` & `(-8, 1)`

`=\frac{-1}{\text{slope of line passing through the points (1, 2) & (-8, 1) }}`

`=\frac{-1}{\frac{2-1}{1-(-8)}}`

`=\frac{-1}{1/9}`

`=-9`

Answer 2

`"perpendicular slope "=-9`

Explanation:

`"calculate the slope m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(1,2)" and "(x_2,y_2)=(-8,1)`

`m=(1-2)/(-8-1)=(-1)/(-9)=1/9`

`"the slope of a line perpendicular to this is"`

`•color(white)(x)m_("perpendicular")=-1/m=-1/(1/9)=-9`