Answer:
5y - 6x = 53
Explanation:
Given the segment with endpoints M(−3, 7) and N(9, −3), let us find the slope first
m = y2-y1/x2-x1
m = -3-7/9-(-3)
m = -10/12
m = -5/6
Since the unknown line forms a perpendicular bisector, the slope of the unknown line will be:
m = -1/(-5/6)
m = 6/5
To get the intercept of the line, we will substitute m = 6/5 and any point on the line say (-3, 7) into the equation y = mx+c
7 = 6/5 (-3)+c
7 = -18/5 + c
c = 7 + 18/5
c = (35+18)/5
c = 53/5
Substitute m = 6/5 and c = 53/5
y = 6/5 x + 53/5
multiply through by 5
5y = 6x + 53
5y - 6x = 53
hence the point-slope equation of the perpendicular bisector is 5y - 6x = 53