1. The document provides examples of using the distance and midpoint formulas to calculate the distance between two points and find the midpoint between two points on a coordinate plane. 2. It gives the formulas for distance (d=(x2-x1)2+(y2-y1)2) and midpoint ((x1+x2)/2,(y1+y2)/2) and works through examples of using each. 3. It also includes a word problem example about meeting a friend in Washington D.C. where the midpoint formula is used to determine which landmark is closest to meet at.

1. P. 740 1-15, 35
16 pts.

2. P. 740 1-15, 35
1. Hypotenuse
2. If the sum of 9 squared and 12 squared
is 15 squared, then it is a right triangle. If
they are not equal, then it is not a right
triangle.
3. b = 4
4. a = 6.3
5. c = 7.8

3. 6. a = 8.7 14. b = 3.5
7. c = 11.3 15. C 85.9 feet
8. c = 13
9. c = 14.4
10. b = 24
11. a=8
12. b = 40
13. a = 1.6 16 pts total

4. Distance & Midpoint Formulas
11.5
P. 744

5. • In this section, you will
– learn how to find the distance between two
point in a coordinate plane
– Learn how to find the midpoint between two
point in a coordinate plane
Both use formulas to calculate the answer.

6. • Distance Formula
2 2
d ( x2 x1 ) ( y2 y1 )
• Midpoint Formula x1 x2 y1 y2
( , )
2 2

7. Distance Formula
• Find the distance between (1,4) & (-2,3)
2 2
d ( x2 x1 ) ( y2 y1 )
• D is about 3.16

8. EXAMPLE 1 Find the distance between two points
Find the distance between (– 1, 3) and (5, 2)
d = ( x2 – x1 ) 2 + ( y2 – y1 ) 2 Distance formula
= (5 – (–1))2 + ( 2 – 3)2 Substitute.
= 62 + (– 1)2 = 37 Simplify.
ANSWER
The distance between the points is 37 units.

9. Find the distance between (3, -1) and (4,0)
2 2
d ( x2 x1 ) ( y2 y1 )

10. • Decide whether the
point (3,2), (2,0) (-1,4)
are vertices of a right
triangle.
• d1
• d2
• d3

11. Midpoint Formula
• The midpoint between
(x1,y1) and (x2,y2) is: x1 x2 y1 y2
( , )
2 2
• Find the midpoint
between (-2,3) & (4,2)
• Check with a graph
• (1, 2 ½)

12. Midpoint Formula
x1 x2 y1 y2
( , )
2 2
Find the midpoint between
(5, -1) and (-3, 7)
Find the midpoint between
(-1,2) and (7,4)

13. EXAMPLE 3 Standardized Test Practice
SOLUTION
Let ( x1, y1 ) = ( –1, – 2) and ( x2, y2 ) = ( 3, – 4 ).
x1 + x2 , y1 + y2 – 1 + 3 ,– 2 + (– 4)
( 2 2 )=( 2 2 ) Substitute
= (1,– 3) Simplify
ANSWER
The correct answer is B.

14. • Find the midpoint of (-4,1) and (2,-3)
• (-1,-1)

15. • Assignment: P. 747
3-10, 22-27
Make sure you put formulas - followed by work for
each problem. Round to the tenths
• Semester Test will be ….
Do some reviewing this next week! Also, we’ll be working
different word problems on RTD

16. P. 747 3-10, 22-27
3. 1 22. (4,2)
4. 3
23. (5,-5)
5. 5
6. 5.4 24. (-2,7)
7. 7.3 25. (1,-4)
8. 8.1
26. (-1,1)
9. 8.2
10. 16.3 27. (-11,-6) 14 pts

17. Determine if the
points (-2,3) (-1,1)
and (2,3) are
vertices of a right
triangle.

18. EXAMPLE 4 Solve a real-world problem
SIGHTSEEING
You and a friend are sightseeing in Washington, D.C.
You are at the National Gallery of Art, and your friend
is at the Washington Monument, as shown on the
map. You want to meet at the landmark that is closest
to the midpoint of your locations. At which landmark
should you meet?

19. EXAMPLE 4 Solve a real-world problem
SOLUTION
Your coordinates are (11, 3), and your friend’s
coordinates are (2, 2). First, find the midpoint of your
locations, which is
x1 + x2 , y1 + y2 11 + 2 , 3+2
( 2 2 )= ( 2 2 ) = (6.5, 2.5).
Next, find the distance from the midpoint to the
Smithsonian Institution, located at (7, 1), and to the
Natural History Museum, located at (7, 3).

20. EXAMPLE 4 Solve a real-world problem
Distance to Smithsonian Institution:
d = (6.5 – 7)2 + (2.5 – 1)2 1.58 units
Distance to Natural History Museum:
d = (6.5 – 7)2 + (2.5 – 3)2 0.71 unit
ANSWER
You should meet at the Natural History Museum.

21. • Worksheet 11.5
• 1-6, 16-21, 22-24, 28
• You may want to put work in your
notebook.

22. Wksh 11.5 1-6,16-24,28
17.(-8.5,8) 28.About 14-15
1. 2.2 18. (-1, -9.5) miles
2. 3.2 19. (5.5, -1.5) 16 points
3. 7.1
20. (25, 0) Extra Cr
4. 10
21.(-1.5, 2) 28.
5. 6.1
22.Yes a.(1750,2000)
6. 10.4
23.Yes b. 1953 ft
16. (3, 8.5)
24.No 28. 8.5 Books