What set of transformations are applied to parallelogram ABCD to create A'B'C'D'?

Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at negative 2, 1.
Second parallelogram transformed formed by ordered pairs A prime at 4, negative 1, B prime at 3, negative 2, C prime at 1, negative 2, D prime at 2, negative 1.

A) Reflected over the x-axis and reflected over the y-axis
B) Reflected over the y-axis and rotated 180°
C) Reflected over the x-axis and rotated 90° counterclockwise
D) Reflected over the y-axis and rotated 90° counterclockwise

Let's choose a specific point/vertex on both parallelogram and see the changes;

Observing that A is (-4, 1) and A' is (4, -1).

From this we can observe that the graph was flipped over the x-axis because the x value went from negative to positive. Again, we see that the shape was flipped over the y-axis since the y values went from positive to negative.

From this scenario, the correct solution should be A.

Double check this by picking another vertex and comparing.

D's coordinates are (-2, 1) and D' is (2, -1)

Again, the x and the y values are flipped, meaning that this graph was flipped over the x-axis and y-axis, confirming our answer.

Hope I helped :)

xero099 xero099 · Answer 2 · 2021-09-24T18:18:57+02:00

We must reflect over the x-axis and then reflect over the y-axis to map parallelogram ABCD onto parallelogram A'B'C'D'. (Choice A)

In this question we must determine the transformation rules to map parallelogram ABCD onto parallelogram A'B'C'D'.

Let be [tex]A(x, y) = (-4, 1)[/tex], [tex]B(x,y) = (-3,2)[/tex], [tex]C(x,y) = (-1,2)[/tex], [tex]D(x,y) = (-2,1)[/tex], [tex]A'(x,y) = (4, -1)[/tex], [tex]B(x,y) = (3, -2)[/tex], [tex]C'(x,y) = (1, -2)[/tex] and [tex]D'(x,y) = (2, -1)[/tex], we must apply the following transformations:

1) Reflection over the x-axis.

[tex]A''(x,y) = (-4,1) - 2\cdot (0, 1)[/tex]

[tex]A''(x,y) = (-4, -1)[/tex]

[tex]B''(x,y) = (-3, 2) -2\cdot (0, 2)[/tex]

[tex]B''(x,y) = (-3, -4)[/tex]

[tex]C''(x,y) = (-1, 2) -2\cdot (0, 2)[/tex]

[tex]C''(x,y) = (-1,-2)[/tex]

[tex]D''(x,y) = (-2, 1) - 2\cdot (0, 1)[/tex]

[tex]D''(x,y) = (-2, -1)[/tex]

2) Reflection over the y-axis.

[tex]A'(x,y) = (-4,-1) -2\cdot (-4, 0)[/tex]

[tex]A'(x,y) = (4, 1)[/tex]

[tex]B'(x,y) = (-3, -4) -2\cdot (-3, 0)[/tex]

[tex]B'(x,y) = (3, -4)[/tex]

[tex]C'(x,y) = (-1,-2) -2\cdot (-1, 0)[/tex]

[tex]C'(x,y) = (1, -2)[/tex]

[tex]D'(x,y) = ( -2,-1) -2\cdot (-2, 0)[/tex]

[tex]D'(x,y) = (2, -1)[/tex]

In a nutshell, we must reflect over the x-axis and then reflect over the y-axis to map parallelogram ABCD onto parallelogram A'B'C'D'.

We kindly invite to check this question on transformation rules: https://brainly.com/question/17478764