Find the midpoint of a line segment

1
EXAMPLE 3
Find the midpoint of a line segment
SOLUTION
Let ( x1, y1 ) (5, 1) and ( x2, y2 ) (1, 6).
2
EXAMPLE 4
Find a perpendicular bisector
SOLUTION
(1, 5)
3
EXAMPLE 4
Find a perpendicular bisector
STEP 2
4
4
EXAMPLE 4
Find a perpendicular bisector
y 5 4(x 1),
5
EXAMPLE 5
Solve a multi-step problem
Asteroid Crater
6
EXAMPLE 5
Solve a multi-step problem
SOLUTION
y x 34
y 3x 110
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EXAMPLE 5
Solve a multi-step problem
y x 34
Write first equation.
3x 110 x 34
Substitute for y.
4x 76
Simplify.
x 19
Solve for x.
y (19) 34
Substitute the x-value into the first equation.
y 53
Solve for y.
The center of the circle is C (19, 53).
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EXAMPLE 5
Solve a multi-step problem
Use (x1, y1) (0, 0) and (x2, y2) (19, 53).
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for Examples 3, 4 and 5
GUIDED PRACTICE
For the line segment joining the two given
points, (a) find the midpoint and (b) write an
equation for the perpendicular bisector.
3. (0, 0), (24, 12)
(2, 6)
4. (2, 1), (4, 7)
(1 , 7)
10
for Examples 3, 4 and 5
GUIDED PRACTICE
For the line segment joining the two given
points, (a) find the midpoint and (b) write an
equation for the perpendicular bisector.
5. (3, 8), (5, 10)
(1, 1).
ANSWER
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EXAMPLE 4
for Examples 3, 4 and 5
GUIDED PRACTICE
The points (0, 0), (6, 22), and (16, 8) lie on a
circle. Use the method given in Example 5 to find
the diameter of the circle.
6.
SOLUTION
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