1. Use Midpoint and Distance Formulas
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
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

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

4. Warm-Up
5. Find √5 + √20 to the nearest hundredth.
ANSWER
6.71

5. Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
Example 1
Skateboard
In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY.
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.

6. Point M is the midpoint of VW . Find the length of VM . ALGEBRA
Example 2
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.

7. Example 2
Point M is the midpoint of VW . Find the length of VM .
ALGEBRA
SOLUTION
STEP 2
Evaluate the expression for VM when x = 4.
VM = 4x – 1 = 4(4) – 1 = 15
So, the length of VM is 15.
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

8. Guided Practice
In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. 1. 3 4
ANSWER
MN;

9. Guided Practice
In Exercises 1 and 2, identify the segment bisector of PQ . Then find PQ. 2.
line ; 11 5 7
ANSWER

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

11. Example 3
b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.
SOLUTION
b. 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

12. Guided Practice
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)

13. Example 4
SOLUTION
Use the Distance Formula. You may find it helpful to draw a diagram.

14. Example 4 SOLUTION (x – x ) + (y – y ) RS = [(4 – 2)] + [(–1) –3] =
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

15. Guided Practice
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

16. Guided Practice
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

17. Lesson 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

18. Lesson 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)

19. Lesson 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