Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'? a dilation with a scale factor of One-fourth and then a rotation a dilation with a scale factor of One-fourth and then a translation a dilation with a scale factor of 4 and then a rotation a dilation with a scale factor of 4 and then a translation

The composition of similarity transformations maps polygon ABCD to polygon A'B'C'D' is a dilation with a scale factor of One-fourth and then a translation.

Given :

The following steps can be used in order to determine the correct composition of transformation:

Step 1 - Let the dilation factor be '1/4'.

Step 2 - So, after the dilation the coordinates of polygon ABCD becomes:

A*(-3/4,3/4), B*(5/4,3/4), C*(5/4,-1/4), and D*(1/4,-5/4)

Step 3 - Now, translate the polygon A*B*C*D* by a factor of 17/4. So, the coordinates of the polygon A*B*C*D* become:

A'(-5,2), B'(-3,2), C'(-3,-3), and D'(-4,-4)

Therefore, the correct option is B).

For more information, refer to the link given below:

link

a dilation with a scale factor of 4 and then a translation

Step-by-step explanation:

Given that the vertices of polygon ABCD are at A(-3, 3), B(5, 3), C(5, -1), D(1, -5) while the vertices of polygon A'B'C'D' are at A'(-5, -2), B'(-3, 2), C'(-3, -3), D(-4, -4)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is a type of transformation that enlarges or reduces an object thereby producing an image which has the same shape but a different size as the object. If a point X(x, y) is dilated by a factor k, the new location is X'(kx, ky).

If a point X(x, y) is translated a units left and b units down, the new location is X'(x - a, y - b)

If polygon ABCD is dilated by a factor of One-fourth, the new point is A*(-3/4, 3/4), B*(5/4, 3/4), C*(5/4, -1/4), D*(1/4, -5/4), if it is then translated 17/4 units left and 11/4 units down, the new location is A'(-5, -2), B'(-3, 2), C'(-3, -3), D(-4, -4)