Question

What is the slope of any line perpendicular to the line passing through `(9,15)` and `(7,2)`?

Answer 1

`-2/13`

Explanation:

Let the slope of the line joining the 2 points be `m` and the slope of the line perpendicular to it be `m_1`.

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

`m=(15-2)/(9-7)=13/2`

We know, `mm_1=-1`

So `m_1=-2/13` [ANS]

Answer 2

`"perpendicular slope "=-2/13`

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)=(9,15)" and "(x_2,y_2)=(7,2)`

`rArrm=(2-15)/(7-9)=(-13)/(-2)=13/2`

`"Given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

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

`rArr"perpendicular slope "=-1/(13/2)=-2/13`