Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (2,7) and (-6,3).

A) y = -x + 5
B) y = 2x + 5
C) y = -2x - 5
D) I cannot answer this question.

Answer 1

To find the equation of the perpendicular bisector of a line segment, we need to find the midpoint of the line segment and the negative reciprocal of its slope. The midpoint of the line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. The slope of the line segment can be found using the formula (change in y)/(change in x). The negative reciprocal of the slope is -2. So, the equation of the perpendicular bisector is y = -2x + 5.

Step-by-step explanation:

To find the equation of the perpendicular bisector of a line segment, we need to find the midpoint of the line segment and the negative reciprocal of its slope. The midpoint of the line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. So, the midpoint is (2+(-6))/2, (7+3)/2 = (-2, 5).

The slope of the line segment can be found using the formula (change in y)/(change in x). So, the slope is (3-7)/(-6-2) = -4/(-8) = 1/2.

The negative reciprocal of the slope is -2. So, the equation of the perpendicular bisector is y = -2x + 5.