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Warm-up
6th Hour – Chapter 6 Test Scores:
100, 98, 95, 94, 92, 92, 88, 85, 83, 82, 72,
70, 67, 66, 62, 58, 7
Mean
Median
Mode
Range
What happens to the mean if you take the 7
out of the data set?
Section 9-1
Apply the Distance and
Midpoint Formulas
Vocabulary
• Distance Formula – The distance between (x1, y1)
and (x2, y2) is d = √(x2 – x1)2 + (y2 – y1)2
• Midpoint Formula –
x1 + x2 , y1 + y2
2
2
• Scalene Triangle – No sides equal
• Isosceles Triangle – Two sides equal
• Equilateral Triangle – All sides equal
Example 1
What is the distance between (-5, 1) and (-3, 2)?
(x1 , y1)
(x2 , y2)
d = √(x2 – x1)2 + (y2 – y1)2
d = √(-3 – (-5))2 + (2 – 1)2
d = √(2)2 + (1)2
d=√5
Example 2
Find the midpoint of the segment joining
(-2, 3) and (4, -2).
(x1 , y1)
(x2 , y2)
x1 + x2 , y1 + y2
2
2
-2 + 4 , 3 + (-2)
2
2
2, 1
1, 1
2 2 =
2
Example 3
Write an equation for the perpendicular bisector of
the line segment joining A (5, 4) and B (-1, 6).
(x1 , y1)
(x2 , y2)
x1 + x2 , y1 + y2
2
2
5 +(-1) , 4 + 6
2
2
4 , 10
=
2
,
5
2 2
Step 1: Find the midpoint
of the line segment.
Example 3 - Continued
Write an equation for the perpendicular bisector of
the line segment joining A (5, 4) and B (-1, 6).
(x1 , y1)
(x2 , y2)
y2 – y1
m= x –x
2
1
6–4
m = -1 – 5
m=
-1/
3
Step 2: Calculate the slope
of AB.
Example 3 - Continued
Write an equation for the perpendicular bisector of
the line segment joining A (5, 4) and B (-1, 6).
m =3
2, 5
y – y1 = m(x – x1)
y – 5 = 3(x – 2)
y – 5 = 3x – 6
y = 3x – 1
Step 3: Find the slope of
the perpendicular bisector.
Step 4: Use point-slope
form to find the equation.
Homework
Section 9-1
Pages 617 –618
4, 7, 10, 12, 18,
19, 22, 25, 32,
35, 36, 41