Question

What's the equation of the line that's a perpendicular bisector of the segment connecting C (6, –12) and D (10, –8)? answers: A) y = –x – 2 B) y = x + 2 C) y = –1∕2x – 2 D) y = 2x – 6

Answer 1

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= $( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

Thus, midpoint of CD

$= ( \frac{6 + 10}{2} , \frac{ - 12 - 8}{2} ) \\ = ( \frac{16}{2} , \frac{ - 20}{2} ) \\ = (8, - 10)$

Gradient of line CD

$= \frac{y1 - y2}{x1 - x2} \\ = \frac{ - 12 - ( - 8)}{6 - 10} \\ = \frac{ - 12 + 8}{ - 4} \\ = \frac{ - 4}{ - 4} \\ = 1$

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.