Quadrilateral Dilation and Scale Factor

What is the scale factor of a dilation from quadrilateral EFGH to quadrilateral QRST?

Scale factor: 2

Quadrilateral EFGH is dilated with a center at (0, 0) to produce quadrilateral QRST. The scale factor of this dilation is 2, which indicates that the image (quadrilateral QRST) is twice as large as the original (quadrilateral EFGH).

The scale factor of a dilation is determined by the ratio of the corresponding side lengths of the original figure (quadrilateral EFGH) and the image after dilation (quadrilateral QRST). Since the center of dilation is at (0, 0), the coordinates of the image (QRST) are twice the coordinates of the original (EFGH) due to dilation by a factor of 2 enlarging the figure.

Therefore, the scale factor for each pair of corresponding sides, such as QR/EF, RS/FG, ST/GH, and TQ/HE, is calculated to be 2.

So, the scale factor of this dilation is indeed 2, as represented by option b). This demonstrates that the dilation transforms quadrilateral EFGH into quadrilateral QRST with a scale factor of 2.

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