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P. 740 1-15, 35
16 pts.
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
6. a = 8.77. c = 11.38. c = 139. c = 14.410. b = 2411. a = 812. b = 4013. a = 1.6
14. b = 3.5
15. C 85.9 feet
16 pts total
Distance & Midpoint Formulas
11.5
P. 744
• 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.
• Distance Formula
• Midpoint Formula1 2 1 2( , )
2 2
x x y y
2 22 1 2 1( ) ( )d x x y y
Distance Formula
• Find the distance between (1,4) & (-2,3)
• D is about 3.16
2 22 1 2 1( ) ( )d x x y y
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 units.37
2 22 1 2 1( ) ( )d x x y y
Find the distance between (3, -1) and (4,0)
• Decide whether the point (3,2), (2,0) (-1,4) are vertices of a right triangle.
• d1
• d2
• d3
Midpoint Formula
• The midpoint between (x1,y1) and (x2,y2) is:
• Find the midpoint between (-2,3) & (4,2)
• Check with a graph• (1, 2 ½)
1 2 1 2( , )2 2
x x y y
Midpoint Formula
1 2 1 2( , )2 2
x x y y
Find the midpoint between
(5, -1) and (-3, 7)
Find the midpoint between
(-1,2) and (7,4)
EXAMPLE 3 Standardized Test Practice
SOLUTION
Let ( x1, y1 ) = ( –1, – 2) and ( x2, y2 ) = ( 3, – 4 ).
( )x1 + x2 y1 + y2
2 2, = ( )
– 1 + 3 – 2 + (– 4) 2 2
, Substitute
= (1,– 3) Simplify
ANSWER
The correct answer is B.
• Find the midpoint of (-4,1) and (2,-3)
• (-1,-1)
• 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
P. 747 3-10, 22-27
3. 1 4. 35. 56. 5.47. 7.38. 8.19. 8.210. 16.3
22. (4,2)
23. (5,-5)
24. (-2,7)
25. (1,-4)
26. (-1,1)
27. (-11,-6) 14 pts
Determine if the points (-2,3) (-1,1) and (2,3) are vertices of a right triangle.
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?
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
2 2( ), ( ) 11 + 2 3 + 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).
EXAMPLE 4 Solve a real-world problem
ANSWER
You should meet at the Natural History Museum.
Distance to Smithsonian Institution:
d =
(6.5 – 7)2 + (2.5 – 1)2
1.58 units
Distance to Natural History Museum:
0.71 unit(6.5 – 7)2 + (2.5 – 3)2d =
• Worksheet 11.5
• 1-6, 16-21, 22-24, 28
• You may want to put work in your notebook.
Wksh 11.5 1-6,16-24,28
1. 2.2
2. 3.2
3. 7.1
4. 10
5. 6.1
6. 10.4
16. (3, 8.5)
17.(-8.5,8)
18. (-1, -9.5)
19. (5.5, -1.5)
20. (25, 0)
21.(-1.5, 2)
22.Yes
23.Yes
24.No
28.About 14-15 miles
16 points
Extra Cr
29. a.(1750,2000)
b. 1953 ft
30. 8.5 Books