Question

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′. Match each vertex of polygon A′B′C′D′ to its coordinates.

Answer 1

A.(1,1) B.(2,-1) C.(3,0)
D.(2,1)

Answer 2

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

Explanation:

It is given that the vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1).

If a figure is reflected across the x-axis, then according to the rule of reflection

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

After that the figure it translated 2 units up to form polygon A′B′C′D′. According to the rule of translation

`(x,y)\rightarrow (x,-y+2)`

The coordinates of image are

`A(1,1)\rightarrow A'(1,-1+2)=A'(1,1)`

`B(2,3)\rightarrow B'(2,-3+2)=B'(2,-1)`

`C(3,2)\rightarrow C'(3,-2+2)=C'(3,0)`

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

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