Question

graph the perpendicular bisector of the graphed segment with the given endpoints. write the equation of the line in slope - intercept form.

1. a(-2,-2) b(-10,4)

Explanation:

Step1: Find the mid - point of segment AB

The mid - point formula is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For $A(-2,-2)$ and $B(-10,4)$, we have $x_1=-2,y_1 = - 2,x_2=-10,y_2 = 4$. Then $M(\frac{-2+( - 10)}{2},\frac{-2 + 4}{2})=M(\frac{-12}{2},\frac{2}{2})=M(-6,1)$.

Step2: Find the slope of segment AB

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. So, $m_{AB}=\frac{4-( - 2)}{-10-( - 2)}=\frac{4 + 2}{-10 + 2}=\frac{6}{-8}=-\frac{3}{4}$.

Step3: Find the slope of the perpendicular bisector

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular bisector be $m_1$. Then $m_1\times(-\frac{3}{4})=-1$, so $m_1=\frac{4}{3}$.

Step4: Find the equation of the perpendicular bisector

Use the point - slope form $y - y_0=m(x - x_0)$ with the point $M(-6,1)$ and $m=\frac{4}{3}$.
$y - 1=\frac{4}{3}(x + 6)$
Expand the right - hand side: $y-1=\frac{4}{3}x+8$.
Add 1 to both sides to get the slope - intercept form: $y=\frac{4}{3}x + 9$.

Answer:

$y=\frac{4}{3}x + 9$