A transformation rule on coordinates can represent a composition, or a single transformation resulting from a sequence of transformations. While the image can be graphed directly from the transformation rule, it is sometimes possible to analyze the rule algebraically to determine the composition before graphing. Find a sequence of transformations resulting in the composition represented by (x,y) → (-2x + 5, 2y + 7). Complete the solution by providing the missing information. Identify transformation rules algebraically. Simplify and compare to the original rule. Following the order of operations, the transformation function first multiplies x by and then adds 5. This can be further broken down into multiplication by then multiplication by 2, with addition of 5 to that result. Meanwhile, y is first multiplied by 2 and then has to that result. added The rule (x,y) → (-x, y) represents a while (x,y) → (2x, 2y) represents a . and (x, y) → (x + 5, y + 7) represents a and by 7 units. across the by a scale factor of. right by Applying the reflection, dilation, and translation in that order gives a rule (x, y) >-(-×0) - (²0-0²)-(²-× +29+7). 2y This transformation rule simplifies to (x, y) 5. 2 --axis, units which is
A transformation rule on coordinates can represent a composition, or a single transformation resulting from a sequence of transformations. While the image can be graphed directly from the transformation rule, it is sometimes possible to analyze the rule algebraically to determine the composition before graphing. Find a sequence of transformations resulting in the composition represented by (x,y) → (-2x + 5, 2y + 7). Complete the solution by providing the missing information. Identify transformation rules algebraically. Simplify and compare to the original rule. Following the order of operations, the transformation function first multiplies x by and then adds 5. This can be further broken down into multiplication by then multiplication by 2, with addition of 5 to that result. Meanwhile, y is first multiplied by 2 and then has to that result. added The rule (x,y) → (-x, y) represents a while (x,y) → (2x, 2y) represents a . and (x, y) → (x + 5, y + 7) represents a and by 7 units. across the by a scale factor of. right by Applying the reflection, dilation, and translation in that order gives a rule (x, y) >-(-×0) - (²0-0²)-(²-× +29+7). 2y This transformation rule simplifies to (x, y) 5. 2 --axis, units which is
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
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Complete the solution by providing the missing information.
Transcribed Image Text:A transformation rule on coordinates can represent a composition, or a single
transformation resulting from a sequence of transformations. While the image can
be graphed directly from the transformation rule, it is sometimes possible to analyze
the rule algebraically to determine the composition before graphing.
Find a sequence of transformations resulting in the composition represented by
(x,y) → (-2x + 5, 2y + 7).
Complete the solution by providing the missing information.
Identify
transformation rules
algebraically.
Simplify and compare
to the original rule.
Confirm.
Following the order of operations, the transformation function first multiplies
x by
and then adds 5. This can be further broken down into
multiplication by
then multiplication by 2, with addition of 5 to
that result. Meanwhile, y is first multiplied by 2 and then has.
to that result.
added
The rule (x,y) → (-x, y) represents a
while (x, y) → (2x, 2y) represents a
and (x, y) → (x + 5, y + 7) represents a
by 7 units.
and
Applying the reflection, dilation, and translation in that order gives a rule
(x,y) →
-(-x) - (²00₂) - (²-x) +₁2y + 7).
-X,
This transformation rule simplifies to (x, y) →
the original rule.
Preimage
A(-4,5)
B(-8,5)
c(-10, 2)
D(-2,2)
Apply the rule to trapezoid ABCD with coordinates A(-4, 5), B(−8, 5),
C(-10, 2), and D(-2, 2), and check the composition against the transformation
rule. This step could be done first to gain some insight.
Image
A(13.0
A 13,
B'
across the
by a scale factor of.
right by
c/25.0
D'
x+ 5, 2y +
-axis,
units
which is
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