Question

ANSWER FAST WILL MARK BRANLIEST 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 − 3, y + 4) 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

Answers:

Point A' is located at (-5, 6)

Point B' is located at (-5, 8)

Point C' is located at (-1, 8)

Point D' is located at (-1, 6)

The line segments AA' and BB' and CC' and DD' are all parallel. The four line segments are also the same length.

see the attached image below

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Explanation:

Point A is located at (-2,2). We subtract 3 from the x coordinate to move 3 spots to the left and we end up at (-5,2). Finally we move up 4 units, so add 4 to the y coordinate to finally land at point A' (-5, 6). This move of "shift left 3, up 4" is applied to the other three points as well.

B moves from (-2,4) to (-5,4) and then (-5,8) which is the location of B'

Same for C. We start at (2,4), move to (-1,4) and then (-1,8)

Finally D we start at (2,2), move to (-1,2) and then land on (-1,6)

This is all shown in the attached image below. Connect the lines from A to A', from B to B', C to C' and D to D'. These lines are shown in blue. They are all parallel and are the same length.

To prove they are parallel, you would use the slope formula to prove they have the same slope value. To show they are the same length, use the distance formula to show that the distance from A to A' is the same as the distance from B to B', etc etc.