Compositions of Transformations Quick Check
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Question
Use the image to answer the question.
Two triangles, upper A upper B upper C and upper D upper E upper F, are graphed on a coordinate plane. The x-axis ranges from negative 5 to 6 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Determine the congruence transformation used on △ABC that resulted in △DEF.
(1 point)
Responses
△ABC was shifted 2 units to the left and 2 units up, then reflected across the y-axis.
triangle upper A upper B upper C was shifted 2 units to the left and 2 units up, then reflected across the y -axis.
△ABC was rotated −180° (clockwise) or 180° (counterclockwise), then shifted 2 units to the right and 2 units up.
triangle upper A upper B upper C was rotated negative 180 degrees (clockwise) or 180 degrees (counterclockwise), then shifted 2 units to the right and 2 units up.
△ABC was shifted 2 units to the right and 2 units up, then rotated 180° (counterclockwise).
triangle upper A upper B upper C was shifted 2 units to the right and 2 units up, then rotated 180 degrees (counterclockwise).
△ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up.
triangle upper A upper B upper C was reflected across the y -axis, then shifted 2 units to the right and 2 units up.
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The correct answer is: △ABC was shifted 2 units to the right and 2 units up, then reflected across the y-axis.
To determine the congruence transformation used on △ABC that resulted in △DEF, we analyze the given answer choices:
- Choice 1: △ABC was shifted 2 units to the left and 2 units up, then reflected across the y-axis.
- Choice 2: △ABC was rotated −180° (clockwise) or 180° (counterclockwise), then shifted 2 units to the right and 2 units up.
- Choice 3: △ABC was shifted 2 units to the right and 2 units up, then rotated 180° (counterclockwise).
- Choice 4: △ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up.
Analyzing the image, it appears that △ABC was reflected across the y-axis first and then shifted 2 units to the right and 2 units up. So, the correct answer is:
- △ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up.
Therefore, the correct answer is: "triangle upper A upper B upper C was reflected across the y-axis, then shifted 2 units to the right and 2 units up."