1. August 29, 2016 1. Find a point between A(–3, 5) and B(7, 5).
ANSWER
Sample: (2, 5)
2. Find the average of –11 and 5.
ANSWER –3

2. 3. Solve = 5. 2
x + 7
ANSWER 3
4. Find √30 to the nearest hundredth.
ANSWER
5.48

3. 5. Find √5 + √20 to the nearest hundredth.
ANSWER
6.71

5. 1.3 Use Midpoint and Distance Formulas
WARM - UP

6. Measure the distance between the endpoints and the midpoint.
What do you notice?

7. Vocabulary midpoint – the point that divides the segment into two
congruent segments
segment bisector – a point, ray, line, line segment, or plane
that intersects the segment at its midpoint

8. Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
EXAMPLE 1
Find segment lengths
In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY.
Skateboard
SOLUTION
Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
XY = XT + TY
Segment Addition Postulate =
Substitute.
= 79.8 cm
Add.

9. Use algebra with segment lengths
EXAMPLE 2
Use algebra with segment lengths
Point M is the midpoint of VW . Find the length of VM .
ALGEBRA
SOLUTION
STEP 1
Write and solve an equation. Use the fact that VM = MW.
VM = MW
Write equation.
4x – 1 = 3x + 3
Substitute.
x – 1 = 3
Subtract 3x from each side.
x = 4
Add 1 to each side.
STEP 2
Evaluate the expression for VM when x = 4.
VM = 4x – 1 = 4(4) – 1 = 15
So, the length of VM is 15.

10. EXAMPLE 2
Use algebra with segment lengths
Check: Because VM = MW, the length of MW should be 15. If you evaluate the expression for MW, you should find that MW = 15.
MW = 3x + 3 = 3(4) +3 = 15

11. GUIDED PRACTICE
for Examples 1 and 2
In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. 1. 3 4
ANSWER
MN;

12. GUIDED PRACTICE
for Examples 1 and 2
In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. 2.
line l ; 11 5 7
ANSWER

13. Graph Activity Plot (-2, 4) and (3, 4).
Fold the two points and find the midpoint.
Now plot (3, 3) and (3, -2).
Now, find the midpoint between (1, -3) and (4, 2).

14. Graph Activity
Find the midpoint between (1, -3) and (4, 2).

15. The Midpoint Formula
The coordinates of the midpoint of a segment are the averages of the x- and y-coordinates of the endpoints
If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint M of AM has coordinates

16. EXAMPLE 3
Use the Midpoint Formula
a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M.
SOLUTION a. 2 5
1 + 4
– 3 + 2 = , M – 1
The coordinates of the midpoint M are 1 , – 5 2
ANSWER

17. EXAMPLE 3
Use the Midpoint Formula
b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

18. EXAMPLE 3
Use the Midpoint Formula
SOLUTION
FIND ENDPOINT Let (x, y) be the coordinates of endpoint K. Use the Midpoint Formula.
STEP 1
Find x.
STEP 2
Find y.
1+ x 2 =
4+ y 1 2 =
1 + x = 4
4 + y = 2
x = 3
y = – 2
The coordinates of endpoint K are (3, – 2).
ANSWER

19. GUIDED PRACTICE
for Example 3
3. The endpoints of AB are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M.
ANSWER
(4,5)
4. The midpoint of VW is M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V.
ANSWER
(– 6, – 8)

20. WARM - UP
September 1, 2016
1. The endpoints of AB are A(3, -4) and B(-6, 5). Find the coordinates of the midpoint M.
2. The endpoints of AB are A(-4, -8) and B(7, 6). Find the coordinates of the midpoint M.
3. The midpoint of VW is M(-4, – 9). One endpoint is W(8, 4). Find the coordinates of endpoint V.
4. The midpoint of VW is M(5, 10). One endpoint is W(-12, 6). Find the coordinates of endpoint V.

21. Distance Formula
To find the distance between the two points, use the distance formula

22. Distance Formula

23. EXAMPLE 4
Standardized Test Practice
SOLUTION
Use the Distance Formula. You may find it helpful to draw a diagram.

24. Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
(x – x ) + (y – y ) 2 1 RS =
Distance Formula
[(4 – 2)] + [(–1) –3] 2 =
Substitute.
(2) + (–4 ) 2 =
Subtract.
4+16 =
Evaluate powers. 20 =
Add.
4.47 ~ =
Use a calculator to approximate the square root.
The correct answer is C.
ANSWER

25. GUIDED PRACTICE for Example 4
5. In Example 4, does it matter which ordered pair you choose to substitute for (x , y ) and which ordered pair you choose to substitute for (x , y )? Explain. 1 2
No, when squaring the differences in the coordinates, you get the same answer as long as you choose the x and y values from the same point.
SAMPLE ANSWER

26. GUIDED PRACTICE
for Example 4
6. What is the approximate length of AB , with endpoints A(–3, 2) and B(1, –4)?
6.1 units
7.2 units
8.5 units
10.0 units B
ANSWER

27. Daily Homework Quiz
1. AB bisects CD at E. If CE = in., Find CD. 1 4 2 1 2 4
ANSWER
in.
2. Point M is the midpoint of XY. Find XM.
ANSWER 17

28. Daily Homework Quiz
3. Point M is the midpoint of PQ with endpoints P(2, – 6 ) and Q(– 8, 0). Find the coordinates of M.
ANSWER
(–3, –3)
4. The midpoint of GH is M(4, –1). One endpoint is G(5, 3) . Find the coordinates of H.
ANSWER
(3, –5)

29. Daily Homework Quiz
5. To find the distance between the swing and the sandbox in his backyard, Darren made a graph and found the coordinates of the swing to be (7, 2) and the coordinates of the sandbox to be (– 3, 8). Find the distance between the swing and the sandbox to the nearest tenth of a unit.
11.7
ANSWER

30. Class Work Sect. 1.3 #’s 3,4,10,13,18,23,24,25,33,34,36,42, ,47,49,53
Homework Sect. 1.3 #’s 6,8,9,14,20,26,35,45,49,52

32. More Examples
What is the measure of segment PR if Q is the midpoint of segment PR?

33. Answer
If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x
So,
2(6 – 3x) = 14x + 2
12 – 6x = 14x + 2
10 = 20x
x = ½
PR = 14(1/2) + 2 = = 9

34. Last Example
What is the measure of segment AC if B is the midpoint of segment AC?

35. 1.3 Use Midpoint

36. 1.3 Use Midpoint

37. Distance Formula Write this into your foldable
B (x2, y2)
C(x2, y1) •
A(x1, y1)
|x2 – x1|
|y2 – y1|
Find AB
(AB)2 = (x2 – x1)2 + (y2 – y1)2
This formula can be used to find the distance between any two points in the plane

38. 1.3 Distance Formula

39. REMIND
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