Question

Enter an equation in point-slope form for the perpendicular bisector of the segment with endpoints M(−3, 7) and N(9, −3). The point-slope equation of the perpendicular bisector is .

Answer 1

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