Answer: y = 1/4x +1
Explanation:
First, we can find the midpoint of the line segment using the average of x and y coordinates of the endpoints:
M(x,y) = ((-2 + (-6))/2 , (-9 + 7)/2)
M(x,y) = (-4, -1)
To find the slope of the perpendicular bisector, we have to take the negative reciprocal of the slope of the line segment which is (y2-y1)/(x2-x1) = (7-(-9))/(-6-(-2)) = -16/4 = -4
Slope of the perpendicular bisector = -1/slope of the line segment = -1/(-4) = 1/4
Now we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - (-1) = 1/4(x + 4)
y = 1/4x +1
so the equation of the perpendicular bisector of the line segment whose endpoints are (-2,-9) and (-6,7) is y = 1/4x +1