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

Answer:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

Step-by-step explanation:

We have the following points of a quadrilateral ABCD:

A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)

and the rule of the translation is given by:

(x, y) ---> (x + 2, y − 3)

which means that each point will move means  3 units to the left and 4 units upwards.

So the points after transformation will be:

A(−2, 2) ---> (-2+2, 2-3) ---> A' (0, -1)

B(−2, 4) ---> (-2+2, 4-3) ---> B' (0, 1)

C(2, 4) ---> (2+2, 4-3) ---> C' (4, 1)

D(2, 2) ---> (2+2, 2-3) ---> D' (4, -1)

If we plot these points on a graph and join the corresponding vertices with line segments, then we will see that all the the lines will be parallel to each other since they followed the same rule of transformation.