# Find, in terms of x and y , the equation of the perpendicular bisector of the line segment joining the points(-1,2) and (-7,0) . The equation of the perpendicular bisector is .?

Dec 16, 2017

$y = - 3 x - 11$

#### Explanation:

$\text{the perpendicular bisector, bisects the segment at }$
$\text{right angles}$

$\text{mid-point } = \left[\frac{1}{2} \left(- 1 + \left(- 7\right)\right) , \frac{1}{2} \left(2 + 0\right)\right]$

$\textcolor{w h i t e}{\times \times \times \times} = \left(- 4 , 1\right)$

$\text{given a line with slope m then the slope of a line }$
$\text{perpendicular to it is}$

${m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{m}$

$\text{ calculate the slope m using the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(-1,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 7 , 0\right)$

$\Rightarrow m = \frac{0 - 2}{- 7 - \left(- 1\right)} = \frac{- 2}{- 6} = \frac{1}{3}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{\frac{1}{3}} = - 3$

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\Rightarrow y = - 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-4,1)" into the partial equation}$

$1 = 12 + b \Rightarrow b = - 11$

$\text{equation of perpendicular bisector is}$

$y = - 3 x - 11 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$