A''(1, 2)
B''(1, 0)
C''(4, 0)
D''(4, 2)
If we have a point (x,y) on a graph, the way this point can be translated is written as:
[tex](x,y)\rightarrow(x+c,y+k)[/tex]
If k>0 the point is translated k units upward. Since there is no any translation to the left or to the right c = 0, but It is translated 3 units up, then k =3:
[tex](x,y)\rightarrow(x,y+3)[/tex]
Then, each point is translated 3 units up as follows:
A(–1, –1) → A'(–1, –1 + 3) = A'(–1, 2)
B(–1, –3) → B'(–1, –3 + 3) = B'(–1, 0)
C(–4, –3) → C'(–4, –3 + 3) = C'(–4, 0)
D(–4, –1) → D'(–4, –1 + 3) = D'(–4, 2)
Then we need to reflect each point across the y-axis:
Consider the point [tex](x,y)[/tex], if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:
[tex](x,y)\rightarrow(-x,y)[/tex]
Then:
A'(–1, 2) → A''(–1(–1), 2) = A''(1, 2)
B'(–1, 0) → B''(–1(–1), 0) = B''(1, 0)
C'(–4, 0) → C''(–4(–1), 0) = C''(4, 0)
D'(–4, 2) → D''(–4(–1), 2) = D''(4, 2)
