Question

xy is formed by x(-9, -7) and y(-3, 5). if line j is the perpendicular bisector of xy, write a linear equation for j in slope - intercept form. do not leave any spaces when entering answers below. mp of xy: ( ) slope (m) of xy: perpendicular bisector to xy: y =

Explanation:

Step1: Find mid - point

Mid - point formula: $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For $X(-9,-7)$ and $Y(-3,5)$, $(\frac{-9+( - 3)}{2},\frac{-7 + 5}{2})=(-6,-1)$.

Step2: Find slope of $XY$

Slope formula: $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m_{XY}=\frac{5-( - 7)}{-3-( - 9)}=\frac{12}{6}=2$.

Step3: Find slope of perpendicular bisector

The slope of the perpendicular line is the negative reciprocal. So $m_j=-\frac{1}{2}$.

Step4: Find equation of line $j$

Using point - slope form $y - y_1=m(x - x_1)$ with point $(-6,-1)$ and $m =-\frac{1}{2}$, we get $y+1=-\frac{1}{2}(x + 6)$, which simplifies to $y=-\frac{1}{2}x-4$.

Answer:

mp of $XY$: $(-6,-1)$
slope ($m$) of $XY$: $2$
Perpendicular Bisector to $XY$: $y=-\frac{1}{2}x - 4$