Answer: A'(1,1) , B'(2,-1) , C'(3,0) and D'(2,1)
Step-by-step explanation:
The transformation rule for reflection across x axis is given by :-
[tex](x,y)\to(x,-y)[/tex] (1)
The rule for translation h units above is given by :-
[tex](x,y)\to(x,y+h)[/tex] (2)
Given : The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′.
The coordinates of polygon ABCD after reflection across the x-axis Using (1) :
A(1, 1) → (1,-1)
B(2, 3) → (2,-3)
C(3, 2) → (3,-2)
D(2, 1) → (2,-1)
Now, after translation of 2 units up , the coordinates of polygon A′B′C′D′ using (2 ) will be :
(1,-1) → A'(1,-1+2) = A'(1,1)
(2,-3) → B'(2,-3+2) = B'(2,-1)
(3,-2) → C' (3,-2+2) = C'(3,0)
(2,-1) → D'(2,-1+2) = D'(2,1)
Hence, the answer is A'(1,1) , B'(2,-1) , C'(3,0) and D'(2,1),.
