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

Jan 29, 2016

slope = $\frac{11}{7}$

#### Explanation:

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

$\textcolor{b l u e}{\text{ gradient formula }}$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

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

are 2 points.

let $\left({x}_{1} , {y}_{1}\right) = \left(4 , 5\right) \textcolor{b l a c k}{\text{ and }} \left({x}_{2} , {y}_{2}\right) = \left(- 7 , 12\right)$

hence $m = \frac{12 - 5}{- 7 - 4} = \frac{7}{- 11} = - \frac{7}{11}$

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 $- \frac{7}{11} \times {m}_{2} = - 1 \textcolor{b l a c k}{\text{ and }} {m}_{2} = - \frac{1}{- \frac{7}{11}} = \frac{11}{7}$