perpendicular bisector to the line segment

Question

Write the equation of the perpendicular bisector to the line segment with endpoints (3,-5) and (-1,7).

Given line:

New line:

Answer 1

Step 1. Find the (x,y) coordinates of the midpoint of the line segment with the given endpoints:

(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Step 2: Find the slope of the line with the given endpoints

slope = (y₂-y₁) / (x₂-x₁)

Step 3. The perpendicular bisector will have a slope equal to the negative reciprocal of the slope in step 2. So if that slope equals -2, the perpendicular bisector will have a slope of -1/(-2) = 1/2.

Step 4. The perpendicular bisector line has the form y = mx + b. m is the slope you got in step 3. Plug that value into y = mx + b in place of m. To find the value of b, plug in the (x,y) values of the midpoint from step 1 and solve for b. Plug the value you get for b into y =mx+b where the m is the slope from step 2. You're done.

[ Answer: y = (1/3)x + 2/3 ]