1. Splash Screen

2. Five-Minute Check (over Lesson 10–5) Then/Now New Vocabulary
Key Concept: The Distance Formula
Example 1: Distance Between Two Points
Example 2: Real-World Example: Use the Distance Formula
Example 3: Find a Missing Coordinate
Key Concept: The Midpoint Formula
Example 4: Find the Midpoint
Lesson Menu

3. A B C D Find the missing length. A. 72.34 B. 60.46 C. 59.82 D. 55.36
5-Minute Check 1

4. A B C D Find the missing length. A. 19.80 B. 18.72 C. 16.55 D. 14.41
5-Minute Check 2

5. If c is the measure of the hypotenuse of a right triangle, find the missing measure. If necessary, round to the nearest hundredth. a = 5, b = 9, c = ____ ? A B C
D. 8.44 A B C D
5-Minute Check 3

6. If c is the measure of the hypotenuse of a right triangle, find the missing measure b. If necessary, round to the nearest hundredth. a = 6,
A. 15.3
B. 13.7
C. 9.11
D. 6.3 A B C D
5-Minute Check 4

7. The length of the hypotenuse of a right triangle is 26 yards long
The length of the hypotenuse of a right triangle is 26 yards long. The short leg is 10 yards long. What is the length of the longer leg?
A. 10 yd
B. 12 yd
C. 16 yd
D. 24 yd A B C D
5-Minute Check 5

8. You used the Pythagorean Theorem. (Lesson 10–5)
Find the distance between two points on a coordinate plane.
Find the midpoint between two points on a coordinate plane.
Then/Now

9. Distance Formula
midpoint
Midpoint Formula
Vocabulary

10. Concept

11. Find the distance between the points at (1, 2) and (–3, 0).
Distance Between Two Points
Find the distance between the points at (1, 2) and (–3, 0).
Distance Formula
(x1, y1) = (1, 2) and (x2, y2) = (–3, 0)
Simplify.
Evaluate squares and simplify.
Answer:
Example 1

12. A B C D Find the distance between the points at (5, 4) and (0, –2).
A. 29 units
B. 61 units
C units
D. 10 units A B C D
Example 1

13. Use the Distance Formula
BIATHLON Julianne is sighting her rifle for an upcoming biathlon competition. Her first shot is 2 inches to the right and 7 inches below the bull’s- eye. What is the distance between the bull’s-eye and where her first shot hit the target?
Model the situation. If the bull’s-eye is at (0, 0), then the location of the first shot is (2, –7). Use the Distance Formula.
Example 2

14. Distance Formula (x1, y1) = (0, 0) and (x2, y2) = (2, –7) Simplify.
Use the Distance Formula
Distance Formula
(x1, y1) = (0, 0) and (x2, y2) = (2, –7)
Simplify.
Answer:
Example 2

15. HORSESHOES Marcy is pitching a horseshoe in her local park
HORSESHOES Marcy is pitching a horseshoe in her local park. Her first pitch is 9 inches to the left and 3 inches below the pin. What is the distance between the horseshoe and the pin?
A. 6 in.
B. 3 in.
C in.
D in. A B C D
Example 2

16. Find a Missing Coordinate
Find the possible values for a if the distance between the points at (2, –1) and (a, –4) is 5 units.
Distance Formula
d = 5, x2 = a, x1 = 2, y2 = –4, and y1 = –1
Simplify.
Evaluate squares.
Simplify.
Example 3

17. 0 = a2 – 4a – 12 Subtract 25 from each side.
Find a Missing Coordinate
25 = a2 – 4a + 13 Square each side.
0 = a2 – 4a – 12 Subtract 25 from each side.
0 = (a – 6)(a + 2) Factor.
a – 6 = 0 or a + 2 = 0 Zero Product Property
a = a = –2 Solve.
Answer: The value of a is –2 or 6.
Example 3

18. Find the value of a if the distance between the points at (2, 3) and (a, 2) is units.
A. –4 or 8
B. 4 or –8
C. –4 or –8
D. 4 or 8 A B C D
Example 3

19. Concept 2

20. (x1, y1) = (8, –3) and (x2, y2) = (–4, –1)
Find the Midpoint
Find the coordinates of the midpoint of the segment with endpoints at (8, –3) and (–4, –1).
Midpoint formula
(x1, y1) = (8, –3) and (x2, y2) = (–4, –1)
Simplify the numerators.
Simplify.
Answer: (2, –2)
Example 4

21. Find the coordinates of the midpoint of the segment with endpoints at (3, 4) and (7, 2).
B. (2, 3)
C. (–5, –6)
D. (–4, –6) A B C D
Example 4

22. End of the Lesson