What is the equation of the perpendicular bisector of the segment joining points A(2, 2) and B(6, 8)?

Question

A.)  

B.)

 C.)

 D.)

Answer 1

This is a multi-part question which essentially requires you to 1. Find the slope of the line between those two points, 2. Find the perpendicular slope, 3. Find the midpoint between those two points, and finally 4. Find the equation of the line with the perpendicular slope (2) through the midpoint (3).

1. Slope between (2,2) and (6,8): (8-2)/(6-2) = 6/4 = 3/2
2. Perpendicular slope: -1/(3/2) = -2/3
3. Midpoint between (2,2) and (6,8): ((2+6)/2 , (2+8)/2) = (8/2, 10/2) = (4,5)
4. Equation of a line with slope -2/3 through point (4,5): y = (-2/3)x + b ... 5 = (-2/3)4 + b ... 5 = (-8/3) + b ... b = 5+8/3 = 15/3 + 8/3 = 23/3 ... y = (-2/3)x + 23/3

Therefore, the answer is actually C, y = (-2/3)x + 23/3

Answer 2

You need 2 pieces of information to find any line: a point and a slope. The slope of the line segment is (8-2)/(6-2) = 3/2. a line perpendicular to it will have a slope of -2/3. The midpoint of the segment is (4.5). So now we have a point and a slope. To find the equation of the line:

y-5 = -2/3(x-4)

y-5 = -2/3(x) + 8/3

y = -2/3(x) + 23/3