Question

Rectangle ABCD has vertex coordinates A(–1, –1), B(–1, –3), C(–4, –3), and D(–4, –1). It is translated 3 units up and reflected across the y-axis. What are the coordinates of A"B"C"D"?

Answer 1

A''(1, 2)

B''(1, 0)

C''(4, 0)

D''(4, 2)

Explanation:

If we have a point (x,y) on a graph, the way this point can be translated is written as:

`(x,y)\rightarrow(x+c,y+k)`

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:

`(x,y)\rightarrow(x,y+3)`

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
`(x,y)`, if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

`(x,y)\rightarrow(-x,y)`

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)