"quadrilateral abcd underwent a sequence of transformations to give quadrilateral a′b′c′d′. which transformations could have taken place?

a reflection across the x-axis followed by a reflection across the y-axis

a translation 10 units down followed by a translation 8 units to the right

a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis

a reflection across the line y = x followed by a reflection across the line y = -x"

The transformation that had taken place to map Quadrilateral ABCD to Quadrilateral A'B'C'D' is:

     A translation 10 units down followed by a translation 8 units    to the right

We are given a vertices of Quadrilateral ABCD as:

A(-6,4) , B(-6,6) , C(-2,6) , D(-4,4)

Now when translation is  done 10 units down  then the rule that follows this transformation is:

                 (x,y) → (x,y-10)

and coordinate of the transformed image will be:

A(-6,4) → A°(-6,-6)

B(-6,6) → B°(-6,-4)

C(-2,6) → C°(-2,-4)

D(-4,4) → D°(-4,-6)

Now when this image is translated 8 units to the right we obtain image A'B'C'D' and the coordinates of the transformed image follows the rule:

                       (x,y) → (x+8,y)

Hence,

A°(-6,-6) → A'(2,-6)

B°(-6,-4) → B'(2,-4)

C°(-2,-4) → C'(6,-4)

D°(-4,-6) → D'(4,-6)

Hence,

A(-6,4) → A'(2,-6)

B(-6,6) → B'(2,-4)

C(-2,6) → C'(6,-4)

D(-4,4) → D'(4,-6)

x=30

step-by-step explanation:

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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