Question

Parallelogram ABCD is rotated to create image A'B'C'D'. On a coordinate plane, 2 parallelograms are shown. The first parallelogram has points A (2, 5), B (5, 4), C (5, 2), D (2, 3). The second parallelogram has points A prime (5, negative 2), B prime (4, negative 5), C prime (2, negative 5), D prime (3, negative 2). Which rule describes the transformation? (x, y) → (y, –x) (x, y) → (–y, x) (x, y) → (–x, –y) (x, y) → (x, –y)

Answer 1

Answer:

(x,y) → (y,-x)      

Step-by-step explanation:

We are given two parallelograms.

ABCD with coordinates

A=(2,5)

B=(5,4)

C=(5,2)

D=(2,3)

Another parallelogram A'B'C'D' with coordinates

A'=(5,-2)

B'=(4,-5)

C'=(2,-5)

D'=(3,-2)

Now, A is transformed to A' that is (2,5) is transformed to (5,-2)

We see that the y coordinate becomes the x-coordinate after transformation and the negative of x coordinates becomes y coordinate after transformation.

A similar pattern can be seen for the B, C and D.

Thus, the transformation is given by:

(x,y) → (y,-x)

Answer 2

Answer:

(x,y)→(y,-x)

Step-by-step explanation:

Parallelogram ABCD:

A(2,5)

B(5,4)

C(5,2)

D(2,3)

Parallelogram A'B'C'D':

A'(5,-4)

B'(4,-5)

C'(2,-5)

D'(3,-2)

Rule:

A(2,5)→A'(5,-2)

B(5,4)→B'(4,-5)

C(5,2)→C'(2,-5)

D(2,3)→D'(3,-2)

so the rule is

(x,y)→(y,-x)