Page 175 - Math Course 2 (Book 1)

Radical Expressions: The Distance Formula

2
d = (x –x ) + (y – y ) 2 Distance Formula Your Turn!
2
1
2
1
(x , y ) = (0, 0), and Distance Between Two Points
1
1
2
= (2–0) + (–7 – 0) 2 (x , y ) = (2, 7)
2 2 Find the distance between the points at (5, 4) and
2
= 2 + (–7) 2 Simplify. (0, –2).
= 53 or about 7.28 units A. 29 units
B. 61 units
C. 7.81 units
D. 10 units
53
Answer The distance is or about
7.28 inches.
Answer
Find a Missing Coordinate

Example Real World Example

HORSESHOES
Marcy is pitching a horseshoe in her local park. Her
Find the value of a if the distance between the f rst pitch is 9 inches to the left and 3 inches below
points at (2, –1) and (a, –4) is 5 units. the pin. What is the distance between the horse-
shoe and the pin?
2
d = (x –x ) + (y – y ) 2 Distance Formula
2
1
2
1
A. 9 in.
Let d = 5, x = a, B. 3 in.
2
2
5 = (a–2) + (–4 –(–1)) 2 x = 2, y = –4, and C. 12 in.
2
1
y = –1. D. 9.49 in.
1
2
5 = (a–2) + (–3) 2 Simplify. Answer
2
5 = a –4a + 4 + 9 Evaluate squares.
2
5 = a –4a + 13 Simplify.
2
25 = a – 4a + 13 Square each side.
2
0 = a – 4a – 12 Subtract 25 from Find a Missing Coordinate
each side.
Find the value of a if the distance between the
37
0 = (a – 6)(a + 2) Factor. points at (2, 3) and (a, 2) is units.
Zero Product
a – 6 = 0 or a + 2 = 0 A. –4 or 8
Property
B. 4 or –8
a = 6 a = –2 Solve. The value of a C. –4 or –8
is –2 or 6.
D. 4 or 8

Answer –2 or 6 Answer

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