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Study Guide and Intervention (continued) Perpendiculars and Distance Distance Between Parallel Lines The distance between parallel lines is the length

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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 3 36 Glencoe Geometry

Distance From a Point to a Line When a point is

not on a line, the distance from the point to the line is the length of the segment that contains the point and is perpendicular to the line. Construct the segment that represents the distance from E to ? ? ? AF .

Extend ? ??

AF . Draw ? ?? EG ? ? ?? AF .

EG represents the distance from E to ? ?? AF .Exercises Construct the segment that represents the distance indicated.

1. C to ? ??

AB 2. D to ? ?? AB

A C BX ACD BX

3. T to ? ?? RS 4. S to ? ?? PQ

UR S TX RT SPQ X

5. S to ? ??? QR 6. S to ? ?? RT

RT SP Q X XRTSP distance between

M and PQ

QM

AFBEAFGBE

Study Guide and Intervention

Perpendiculars and Distance

Example

3-6 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 3-6

Chapter 3 37 Glencoe Geometry

Study Guide and Intervention (continued)

Perpendiculars and Distance

Distance Between Parallel Lines The distance between parallel lines is the length of a segment that has an endpoint on each line and is perpendicular to t hem. Parallel lines are everywhere equidistant , which means that all such perpendicular segments have the same length. Find the distance between the parallel lines l and m with the equations y = 2x + 1 and y = 2x - 4, respectively. xy O m

Draw a line p through (0, 1) that is

perpendicular to and m. xy O mp (0, 1)

Line p has slope -

1 2 and y-intercept 1. An equation of p is y = - 1 2 x + 1. The point of intersection for p and ? is (0, 1).To find the point of intersection of p and m, solve a system of equations.

Line m: y = 2x - 4

Line p: y = -

1 2 x + 1

Use substitution.

2x - 4 = -

1 2 x + 1

4x - 8 = -x + 2

5x = 10

x = 2

Substitute 2 for

x to find the y -coordinate. y 1 2 x + 1 1 2 (2) + 1 = -1 + 1 = 0

The point of intersection of

p and m is (2, 0).

Use the Distance Formula to find the

distance between (0, 1) and (2, 0). d (x 2 - x 1 2 + (y 2 -y 1 2 (2 - 0) 2 + (0 - 1) 2 ⎷ ? 5

The distance between

and m is ⎷ ? 5 units.

Exercises

Find the distance between each pair of parallel lines with the given equ ations.

1. y = 8 2. y = x + 3 3. y = -2x

y = -3 y = x - 1 y = -2x - 5 11 2 2 5

Example

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