Question

Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. What is the scale factor from Quadrilateral A to Quadrilateral B? (write your answer as a fraction) Find all the corresponding side lengths of quadrilateral B. The side length of 6 in A corresponds to a side length of 2 in B. The side length of 9 in A corresponds to a side length of in B. The side length of 9 in A corresponds to a side length of in B. The side length of 12 in A corresponds to a side length of in B. What is the perimeter of Quadrilateral B? The perimeter of Quadrilateral B is units.

Answer 1

The answer is below

Explanation:

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

Dilation is the increase or decrease in size of a figure. If a figure with point A(x, y) is dilated by a scale factor of k, the new location is at A'(kx, ky). If k > 1, it is an enlargement and if k < 1, it is a reduction.

a) The scale factor from Quadrilateral A to Quadrilateral B = smallest side length of side B / smallest side length of side A = 2 / 6 = 1/3

Scale factor = 1/4= 1 / 3

The side length of 6 in A corresponds to a side length of 2 in B

Side length of B that corresponds with side length of 9 in A = scale factor * 9 = 1/3 * 9 = 3

The side length of 9 in A corresponds to a side length of 3 in B

Side length of B that corresponds with side length of 12 in A = scale factor * 9 = 1/3 * 12 = 4

The side length of 12 in A corresponds to a side length of 4 in B.

c) perimeter of Quadrilateral B = sum of side lengths of quadrilateral B = 2 + 3 + 3 + 4 = 12 units