Question

Points A and A' have symmetry with respect to the line two units above, and parallel to, the x- axis. Graph the points for A', B', C', and D'. When A is (1, 1), A' is...? When B is (-3, 0), B' is...? When C is (3, 4), C' is...? When D is (-2, -1), D' is...?

Answer 1

Assuming all image points have the same symmetry about y=2, each point (x, y) has image (x, 4-y).

A' = (1, 4-1) = (1, 3)
B' = (-3, 4-0) = (-3, 4)
C' = (3, 4-4) = (3, 0)
D' = (-2, 4-(-1)) = (-2, 5)

Answer 2

The vertices of image are A'(1,3), B'(-3,4), C'(3,0) and D'(-2,5).

Explanation:

It is given that the symmetry with respect to the line two units above and parallel to the x- axis. It means the axis of symmetry is y=2.

If a figure a figure reflected about y=2, then

`(x,y)\rightarrow (x,-y+4)`

The coordinated of A are (1,1), so the coordinated of A' are

`A(1,1)\rightarrow A'(1,-1+4)=A'(1,3)`

The coordinated of B are (-3,0), so the coordinated of B' are

`B(-3,0)\rightarrow B'(-3,-0+4)=B'(-3,4)`

The coordinated of C are (3,4), so the coordinated of C' are

`C(3,4)\rightarrow C'(3,-4+4)=C'(3,0)`

The coordinated of D are (-2,-1), so the coordinated of D' are

`D(-2,-1)\rightarrow D'(-2,-(-1)+4)=D'(-2,5)`

Therefore the vertices of image are A'(1,3), B'(-3,4), C'(3,0) and D'(-2,5).