Name ________________________________________ Date __________________ Class__________________
LESSON
11-4
Challenge
Reflecting a Line Across a Line
A reflection is a type of transformation. Lines can be reflected across the
x-axis or the y-axis. However, lines can also be reflected across other lines.
You can explore reflections across the lines y x and y x. The graph
shows the linear function y 2x 4. The line y x is also shown.
Answer the following questions.
1. What are the slope, x-intercept, and y-intercept of the
line y 2x 4?
_____________________
2. At what point do the lines of the two equations intersect?
_____________________
3. On the graph, draw the reflection of the line y
across the line y x.
2x 4
4. What are the slope, x-intercept, and y-intercept of the
reflected line?
_____________________
5. What general pattern do you see in the slope, x-intercept,
and y-intercept for the reflected line comparing it to the original line?
_________________________________________________________________________________________
_________________________________________________________________________________________
6. Write an equation for the reflected line in slope-intercept form.
_____________________
7. On the graph, draw the line y x. Now draw the reflection of the
line y 2x 4 across the line y x.
8. Write an equation for this new line in slope-intercept form.
_____________________
9. Examine the two reflected lines and their equations. What general
statement can you make about these two lines?
_________________________________________________________________________________________
_________________________________________________________________________________________
© Houghton Mifflin Harcourt Publishing Company
278
Holt McDougal Coordinate Algebra
2.
Challenge
1. 2, 2, 4
4.
gx
2. (4, 4)
1
, 4, 2
2
5. The slope is the reciprocal of the slope of
the original line; the x- and y-intercept
values are interchanged.
1
1
8. y
x2
x2
6. y
2
2
1
x 1
5
9. Possible answer: The lines are parallel.
The intercepts have the same values but
opposite signs.
3.
Problem Solving
1. Cp
0.55p 2.25
2. Jp
0.55p 3.5
3. Possible answer: The slopes are the
same so the lines are parallel.
gx
1
x 2
3
4. a. fx
0.014x
b. fx
0.019x
4. y-intercept of Cp is 2.25; y-intercept of
Jp is 3.5; the cost of the cover.
5. The line is shifted up.
6. $1000
7. B
c. Vertical stretch by a factor of
approximately 1.36
Reading Strategies
d. 42,500,000
1. The line is shifted up 2 units.
x 1
2. The line is shifted down 1 unit.
x1
3. No; the two lines are parallel because
their slopes are the same.
5. a. gx
b. fx
c. Vertical shift 2 units down or horizontal
shift 2 units right
4. The line is shifted 2 units to the left.
5. The line is shifted 1 unit to the right.
Review for Mastery
1. 5; 5; 2x 11
12-1 GEOMETRIC SEQUENCES
2. 4; 2x 1 4; 2x 5
3. 3; 2x 1 3; 2x 2 4. 1; x 1; 2x 1
5. gx 2x 8
6. gx
7. gx 2x
8. gx 2x
9.
1 1 1
1
; ; x
4 4 2
4
11. f
1
x
§ 1·
¨3¸
© ¹
8. D
10.
Practice A
1. 4; 256, 1024, 4096
2x 19
2. 10; 100,000, 1,000,000, 10,000,000
1
3. ; 8, 4, 2
2
1 1
2
x; x; x 1
3 3
3
4. 5; 2500, 12,500, 62,500
f 3 x ; 6x 1
5. 2048
6. 384
7. 1792
8. 3; 9; 729
9. 2; 2; 8192
12. gx 10x 5
10. 1.2; 8; $19.91
© Houghton Mifflin Harcourt Publishing Company
A62
Holt McDougal Coordinate Algebra