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Answer: A″ (−1, 2), B″ (1, 1), C″ (1, −1), D″ (−1, −2)
Step-by-step explanation:
- there are basically 2 parts in the question.
- first one is the translation(easier one)
after translation, the corresponding points will be:
A (− 5, 1) --> a(-5+3,1-2) = (-2,-1)
B (−4, 3) --> b(-4+3,3-2) = (-1,1)
C (−2, 3) --> c(-2+3,3-2) = (1,1)
D (−1, 1) --> d(-1+3,1-2) = (2,-1)
- now the second part:
let (x,y) be a point and if it is rotated by ""
then, the new coordinates (x',y') will be :
x'=
y'=
here,
so,
a(-2,-1) --> A"
(since, cos[90]=0, sin[90]=1)
b(-1,1) -->B"(-1cos[90]+1sin[90], -[-1]sin[90]+1cos[90])=(1,1)
c(1,1) --> C"(1cos[90]+1sin[90],-[1]sin[90]+1cos[90]) = (1,-1)
d(2,-1) --> D"(2cos[90]+[-1]sin[90],-2sin[90]+[-1]cos[90]) =(-1,-2)
these are the coordinates after both the transformations.