Which composition of similarity transformations would map polygon ABDC to polygon A'B'D'C'? a dilation with a scale factor greater than 1 and then a translation a dilation with a scale factor greater than 1 and then a rotation a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation

a dilation with a scale factor greater than 1 and then a translation

Step-by-step explanation:

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 k > 1 it is an enlargement and if k < 1 it is a reduction.

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

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

Since polygon A'B'C'D' is larger that polygon ABCD, this is a dilation with a scale factor greater than 1. It is a dilation by a factor of 2 which gives A*(-10, 4), B*(-6,-2), C*(-2, 4), D*(-6, 2), it is then translated 7 units right and 1 unit down to give A'(-3, 3), B'(1, -3), C'(5, 3), D(1, 1)

Video explanation