226k views
3 votes
Find an equation for the perpendicular bisector of the line segment whose endpoints

are (7,4) and (-5,8).

User Gren
by
4.7k points

1 Answer

5 votes

9514 1404 393

Answer:

y = 3x +3

Explanation:

The midpoint of the given segment is a point on the line. That point is ...

M = ((7, 4) +(-5, 8))/2 = (7-5, 4+8)/2 = (1, 6)

The difference between the end points can be helpful in writing the equation.

(-5, 8) -(7, 4) = (-12, 4) = (Δx, Δy)

Then the general form of the equation of the perpendicular bisector can be written as ...

Δx(x -Mx) +Δy(y -My) = 0 . . . . . where midpoint M = (Mx, My)

-12(x -1) +4(y -6) = 0

Dividing by -4 and eliminating parentheses, we have ...

3(x -1) -(y -6) = 0

3x -y +3 = 0 . . . . general form equation for the line

y = 3x +3 . . . . . . slope-intercept form equation

Find an equation for the perpendicular bisector of the line segment whose endpoints-example-1
User Doug Rohrer
by
4.2k points