Question

What is the slope of any line perpendicular to the line passing through `(4,5)` and `(-7,12)`?

Answer 1

slope = `11/7`

Explanation:

the slope of a line joining 2 points can be calculated using the

`color(blue)( " gradient formula ")`

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

where `(x_1 , y_1 ) color(black)( and") (x_2 , y_2 )`

are 2 points.

let `(x_1 , y_1 )= (4 , 5 ) color(black)(" and ") (x_2 , y_2 ) = (-7 , 12)`

hence `m = (12 - 5 )/(- 7 - 4 ) = 7/(-11) = -7/11`

The 'product' of the gradients of perpendicular lines is

`m_1 . m_2 = - 1`

If `m_2` represents the gradient of the perpendicular line .

then `-7/11 xxm_2 = -1 color(black)( " and ") m_2 = -1/(-7/11) = 11/7`