what sequence of transformations will map a triangle from (1,1), (3,1),…
c. Rotation 180 degrees
Aufgabe
what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)?
a. reflection over the y-axis
b. dilation by 0.5, reflection over the y-axis
c. rotation 180 degrees
d. translation 3 units right, reflection over y-axis
Lösungsschritte
-
Understand the question
what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)?
a. reflection over the y-axis
b. dilation by 0.5, reflection over the y-axis
c. rotation 180 degrees
d. translation 3 units right, reflection over y-axis
-
Explanation
Step1: Analyze coordinate transformation
Compare original points $(x,y)$ to new points $(-x,-y)$:
- $(1,1) \to (-1,-1)$, $(3,1) \to (-3,-1)$, $(2,4) \to (-2,-4)$
Step2: Match to transformation rule
A 180° rotation about the origin follows the rule $(x,y) \to (-x,-y)$, which matches the coordinate change.
Step3: Eliminate other options
- Reflection over y-axis: $(x,y) \to (-x,y)$ (does not match $-y$)
- Dilation + y-axis reflection: Scales coordinates first, does not result in $(-x,-y)$
- Translation + y-axis reflection: Shifts coordinates first, does not result in $(-x,-y)$
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Final answer
c. Rotation 180 degrees
Antwort
Explanation
Step1: Analyze coordinate transformation
Compare original points $(x,y)$ to new points $(-x,-y)$:
- $(1,1) \to (-1,-1)$, $(3,1) \to (-3,-1)$, $(2,4) \to (-2,-4)$
Step2: Match to transformation rule
A 180° rotation about the origin follows the rule $(x,y) \to (-x,-y)$, which matches the coordinate change.
Step3: Eliminate other options
- Reflection over y-axis: $(x,y) \to (-x,y)$ (does not match $-y$)
- Dilation + y-axis reflection: Scales coordinates first, does not result in $(-x,-y)$
- Translation + y-axis reflection: Shifts coordinates first, does not result in $(-x,-y)$
Answer
c. Rotation 180 degrees
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
geometry
Education Level
high school
Difficulty
unspecified
Question Type
multiple choice
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:23:53
OCR Text
Show OCR extraction
what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)? a. reflection over the y-axis b. dilation by 0.5, reflection over the y-axis c. rotation 180 degrees d. translation 3 units right, reflection over y-axis
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