Complete the sequence of transformations that produces △X'Y'Z' from △XYZ.
A clockwise rotation ° about the origin followed by a translation units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
Answers
Given : transformations that produces △X'Y'Z' from △XYZ.
A clockwise rotation °______ about the origin followed by a translation ______ units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
To Find : Complete the sequence of transformations that produces △X'Y'Z' from △XYZ.
Solution:
△XYZ
X = ( - 5 , 3)
Y = (-2 , 3)
Z = (-2 , 1)
ΔX'Y'Z'
X' = ( 5 , - 1)
Y' = ( 5 , - 4)
Z' = (3 , - 4)
△XYZ
90° Clock Wise Rotation means
y' = -x , x' = y
=> X'' = ( 3 , 5)
Y'' = ( 3 , 2
Z'' = ( 1, 2)
Then 2 unit Right
=> x' = x + 2
X''' = ( 5 , 5)
Y''' = ( 5 , 2
Z''' = (3, 2)
Then 6 unit Down
=> y' = y - 6
X' = ( 5 , - 1)
Y' = ( 5 , - 4)
Z' = (3 , - 4)
Hence A clockwise rotation 90° about the origin followed by a translation 2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
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Answer:
90° and 2 units
Step-by-step explanation: