Question

Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 2, y − 3) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.

Answer 1

A' (0,-1)  B'(0,1)   C'(4,1)     D'(4,-1)

Answer 2

The figure is shifted 2 units right and 3 units down. The vertices of image are A'(0,-1), B'(0,1), C'(4,1) and D'(4,-1).

Explanation:

The coordinates of quadrilateral ABCD is A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2).

The quadrilateral is transformed by using the rule

`(x,y)\rigtharrow (x+2,y-3)`

The coordinate of vertices of A'B'C'D' are

`A(-2,2)\rightarrow A'(-2+2,2-3)\rightarrow A'(0,-1)`

`B(-2,4)\rightarrow B'(-2+2,4-3)\rightarrow B'(0,1)`

`C(2,4)\rightarrow C'(2+2,4-3)\rightarrow C'(4,1)`

`D(2,2)\rightarrow D'(2+2,2-3)\rightarrow D'(4,-1)`

The figure is shifted 2 units right and 3 units down. The vertices of image are A'(0,-1), B'(0,1), C'(4,1) and D'(4,-1).