Page 581 - Algebra 1

Math Reasoning
Analyze If the pass is intercepted midway between the quarterback and the receiver, what are the coordinates of the player who intercepts the pass?
d = √(x2 -x1) +(y2 -y1)
566 Saxon Algebra 1
Example 5 Application: Football
A coordinate plane can be used to
model positions of players on a
y
football field. 30
20 A quarterback is on the 30-yard line 10
x
at (30, 10). He throws a pass to his
receiver who is on the 50-yard line at
(50, 40). Find the length of the pass as a radical in simplest form. Then use a calculator to estimate the length to the nearest yard.
SOLUTION Use the distance formula to find the distance between the quarterback and his receiver. Substitute (30, 10) for (x1, y1) and (50, 40) for (x2, y2).
= √(50-30) +(40-10)
22 = √ 2 0 + 3 0
= √ 4 0 0 + 9 0 0 = √ 1 3 0 0
= 1 0 √ 1 3 ≈ 3 6
The pass is about 36 yards long.
Lesson Practice
a.
(Ex 1)
b.
(Ex 2)
c.
(Ex 3)
Use the diagram of city streets from Example 1. What is the direct distance (in city blocks) from the corner of C St. and 2nd Ave. to the corner of D St. and 5th Ave.? Give your answer in simplest radical form. Use a calculator to approximate the answer to the nearest whole city block.
Find the distance between the points (-3, -2) and (4, 2). Determine whether quadrilateral PQRS is a rhombus.
d.
(Ex 4)
e.
(Ex 5)
Find the midpoint of the line segment with endpoints (-2, 3) and (4, 7).
Football Use a coordinate plane like the one shown in Example 5. A quarterback is on the 20-yard line at (20, 33). He throws a pass to his receiver, who is on the opponent’s 58-yard line at (58, 15). Find the length of the pass as a radical in simplest form. Then use a calculator to estimate the length to the nearest yard.
22
Distance formula
Substitute.
Simplify inside parentheses.
Simplify powers.
Add.
Simplify. Use a calculator to approximate.
22
y
4
O
-4-2 24 -2 R
-4 S
Q P
x
50 40
R (50, 40) Q (30, 10)
0 20 40 60 80 100