Question

What's the equation of the line that's a perpendicular bisector of the segment connecting c (6, –12) and d (10, –8)? question 20 options:

a) y = x 2
b) y = 2x – 6
c) y = –x – 2
d) y = –1∕2x – 2

Answer 1

The equation of the perpendicular bisector of the segment connecting points C and D is found by determining the midpoint, calculating the slope of CD, and using the point-slope form to find the equation of the perpendicular bisector, which is y = −x - 2. option c is the correct answer.

Step-by-step explanation:

The equation of the line that is the perpendicular bisector of the segment connecting C (6, –12) and D (10, –8) can be found by first determining the midpoint of the segment CD, then finding the slope of CD and using it to determine the slope of the perpendicular bisector, and finally writing the equation of the perpendicular bisector using the point-slope form of a linear equation.

Steps to find the perpendicular bisector:

1. Find the midpoint M of the segment CD by averaging the x-coordinates and y-coordinates of C and D: M = ((6+10)/2, (−12−8)/2) = (8, −10).
2. Calculate the slope of the line CD, which is (−8 − (−12)) / (10 − 6) = 4/4 = 1. The slope of the perpendicular bisector would then be the negative reciprocal of 1, which is −1.
3. Use point-slope form to write the equation of the perpendicular bisector with the slope −1 and passing through point M (8, −10): y - (-10) = −1(x - 8), which simplifies to y = −x + 8 - 10, and further simplifies to y = −x - 2.

Therefore, the equation of the perpendicular bisector of the segment connecting C (6, –12) and D (10, –8) is y = −x - 2.