Warm Up
What is the midpoint of a segment with endpoints at A (2,1) and B (6, 3) ?
Model Problem 1)
Write the equation of the perpendicular bisector that
goes through the line segment with end points of
A (2,1) and B (6, -3)
Model Problem 2)
Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (1, 2) and B (-2,
8)
Practice Problems
1) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (1, 2) and B (-2,
8)
3) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (-5, 4) and B (3, 4)
How to write an equation of a Perpendicular Bisector
Model Problem 1)
Write the equation of the perpendicular bisector that
goes through the line segment with end points of
A (2,1) and B (6, -3)
Step 1) Find the slope of the line segment using the
points given
Step 2) Find the slope of a line that is perpendicular to
the original line segment.
Step 3) Find the midpoint of the original two points
Step 4) Use the midpoint and new slope to solve for
the y-intercept
Step 5) Write the equation using new slope and yintercept
Model Problem 1 ANSWER)
Write the equation of the perpendicular bisector that goes through the line
segment with end points of
A (2,1) and B (6, -3)
Step 1) Find the slope of the line
segment using the points given
Step 2) Find the slope of a line that
is perpendicular to the original line
segment.
1  3 1  3 4


 1
26
4 4
1 1
1     1
1 1
Step 3) Find the midpoint of the
original two points
 2  6 1  3   8 1  3 
,

 ,

2  2 2 
 2
 2 
 4,    4, 1
 2 
Step 4) Use the midpoint and new
slope to solve for the y-intercept
y = mx + b
y  1x  b
1  1 4   b
1  4  b
4  4
5  b
Step 5) Write the equation using
new slope and y-intercept
y  x5
4) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (4, -1) and B (6,
3)
5) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (-1, -2) and B (-2,
-8)
6) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (0, -5) and B (-4, 10)
Homework
1) What is the midpoint of A(4, -2) and B(6, 5)?
2) If the midpoint of a line is ( 10 , 1) and an endpoint is ( 3, -3), what is its other endpoint?
3) Line segment AB has midpoint M. If the coordinates of A are (-3, 2) and the coordinates of M
are (-1, 5), what are the coordinates of B?
4) What is the equation of a line parallel to y = 7x + 12 that goes through the point ( 4 , -2 )?
5) What is the equation of a line perpendicular to y =
3
x + 5 that goes through the point
4
(9,6)?
6) Find the equation of a line through the points (5,2) and (-1 , 14)
7) Find the equation of a line through the points (4,3) and (8,1)
3) Write the equation of the perpendicular bisector that goes
through the line segment with end points of A (-5, 4) and B (3, 4)