Page 578 - Algebra 1

L E S S O N Calculating the Midpoint and Length
86
of a Segment
Warm Up
1. Vocabulary In an ordered pair, the (x-coordinate, y-coordinate)
(20)
Simplify.
2. -3.8 - 5.5
(6)
4. When viewed from the side, a
(85)
indicates the distance up or down from the origin.
skateboard landing ramp looks like a right triangle. What is the actual length of a ramp that is 2 feet tall if the base is 4 feet long? Round your answer to the nearest tenth.
3. (-6 - (-3))2 (4)
2
5. Multiple Choice Identify the coordinates of point A.
(20)
A (4, 2) B (-4, 2) C (2, -4) D (4, -2)
4
y
A
2
O
x
-4
-2
2
4
-2
-4
New Concepts The Pythagorean Theorem is used to find distances that are difficult to measure directly.
Example
1
Calculating Distance Using the Pythagorean Theorem
The diagram shows a grid of city streets. A car travels from point P to point Q by moving east to point R and then south to point Q. What is the direct distance (in city blocks) from point P to point Q?
SOLUTION To find the direct distance (in city blocks) from P to Q, use the Pythagorean Theorem, written in the form (PQ)2 = (PR)2 + (RQ)2.
5th 4th 3rd
2nd 1st
P
R
Q
A B C D E F G
Streets
Math Reasoning
Analyze A crow flies directly from P to Q. How much farther does the car travel than the crow?
(PQ)2 = (PQ)2 =
√(PQ)2 =
(PR)2 + (RQ)2 42 + 32
√ 42 + 32
√
5
Pythagorean Theorem
Substitute 4 for PR and 3 for RQ.
Take the positive square root of each side. Simplify under the radical.
Simplify the square root.
√(PQ) =
2
25
The direct distance from point P to point Q is 5 city blocks.
Online Connection www.SaxonMathResources.com
PQ =
Lesson 86 563
Avenues