Respuesta :
Answer:
A
Step-by-step explanation:
Perpendicular bisector of a line divides the line into 2 equal parts and it is perpendicular to the line.
First let's find the midpoint of CD. The point is where the perpendicular bisector will cut through the line.
midpoint= [tex]( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
Thus, midpoint of CD
[tex] = ( \frac{6 + 10}{2} , \frac{ - 12 - 8}{2} ) \\ = ( \frac{16}{2} , \frac{ - 20}{2} ) \\ = (8, - 10)[/tex]
Gradient of line CD
[tex] = \frac{y1 - y2}{x1 - x2} \\ = \frac{ - 12 - ( - 8)}{6 - 10} \\ = \frac{ - 12 + 8}{ - 4} \\ = \frac{ - 4}{ - 4} \\ = 1[/tex]
The product of the gradients of perpendicular lines is -1.
gradient if perpendicular bisector(1)= -1
gradient of perpendicular bisector= -1
y=mx +c, where m is the gradient and c is the y-intercept.
y= -x +c
Subst a coordinate to find c.
Since the perpendicular bisector passes through the point (8, -10):
When x=8, y= -10,
-10= -8 +c
c= -10 +8
c= -2
Thus, the equation of the perpendicular bisector is y= -x -2.