Question

The graph shows the dilation with respect to the origin of rhombus RHOM. What is the factor of dilation? 2/3 3/4 4/3 3/2

Answer 1

The factor of dilation for rhombus RHOM is 3/2.

Step-by-step explanation:

The factor of dilation is determined by comparing the corresponding side lengths of the original and dilated rhombus. In this case, if the side length of the original rhombus is multiplied by 3/2 to obtain the corresponding side length of the dilated rhombus, it indicates a dilation factor of 3/2.

Each side of the rhombus experiences the same dilation factor because the transformation is with respect to the origin. The distance from the origin to any point on a side of the rhombus is a constant multiple of the original distance, and this constant is the dilation factor.

In mathematical terms, if
`\( AB \)` is a side of the original rhombus and
`\( A'B' \)` is the corresponding side of the dilated rhombus, the relationship is given by
`\( A'B' = (3)/(2) \cdot AB \)`.

This ratio holds true for all sides of the rhombus, confirming that the factor of dilation is indeed 3/2. The graph visually demonstrates the expansion of the rhombus with respect to the origin, and the consistent application of the dilation factor to each side ensures a proportional transformation.