A segment bisector contains the midpoint of the segment. We will use the Midpoint Formula to find the midpoint M of CD.
M( x_1+x_2/2,y_1+y_2/2 )To find the coordinates of the midpoint M, we will substitute (- 4,5) and (2,- 2) for (x_1,y_1) and (x_2,y_2) in the above formula.
A perpendicular bisector is perpendicular to the segment through the midpoint. In order to find the slope of the bisector, we will first find the slope of CD. To do so, we will use the Slope Formula.
m = y_2-y_1/x_2-x_1
Let's substitute (- 4,5) and (2,- 2) for (x_1,y_1) and (x_2,y_2) in the above formula.
The slope of the perpendicular bisector of CD is 76.
Equation of the Perpendicular Bisector
Since we know a point and the slope of the bisector, we will use the point-slope form of a line to write its equation.
y-y_1=m(x-x_1)
Let's substitute 76 for m and the midpoint ( - 1, 32) for (x_1,y_1) in the formula. Later, we will rewrite the equation of the line to obtain it in the slope-intercept form.
