Which composition of similarity transformations maps…

Maths Questions

Which composition of similarity transformations maps polygon ABCD to polygon A’B’C’D’? Options include: a dilation with a scale factor less than 1 followed by a reflection, a dilation with a scale factor less than 1 followed by a translation, a dilation with a scale factor greater than 1 followed by a reflection, or a dilation with a scale factor greater than 1 followed by a translation.

Answer

The correct composition of similarity transformations is: a dilation with a scale factor less than 1 followed by a reflection. Here’s the reasoning: Polygon ABCD is transformed into polygon A’B’C’D’ through a dilation indicated by a scale factor. Since the resulting image is smaller than the original shape, it confirms a dilation with a scale factor less than 1. For example, the coordinates of point D are (0,-4) for polygon ABCD, and (0,-2) for polygon A’B’C’D’. Assuming k is the scale factor, the transformation can be expressed as (x,y) ‚Üí (kx,ky). Thus, we equate (0,-4) with (0,ky) leading to -4k = -2, which gives us k = 1/2. This demonstrates that the scale factor is indeed less than 1. Additionally, after the dilation, the figure is reflected across the y-axis. Therefore, option A is the correct choice: a dilation with a scale factor less than 1 followed by a reflection.

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