Question

a) describe the transformation that maps figure abcd onto its image. b) figure abcd is dilated by a scale factor of blank.

Explanation:

Step1: Identify the transformation type

By observing the graph, we can see that the shape of the figure has remained the same, but its size has changed. This indicates a dilation transformation.

Step2: Calculate the scale - factor

Let's consider the distance between two corresponding points. For example, take point A(0,7) and A'(2,7). The distance from the y - axis to A is 0 and to A' is 2. If we assume the center of dilation is the origin (0,0), the scale factor \(k\) for the x - coordinates can be calculated. Let's take another pair of corresponding points, say D(4,4) and D'(2,4). The distance of D from the y - axis is 4 and of D' from the y - axis is 2. The scale factor \(k=\frac{\text{distance of image point from origin}}{\text{distance of original point from origin}}\). For the x - coordinates of D and D', \(k = \frac{2}{4}=\frac{1}{2}\).

Answer:

a) The transformation is a dilation with the center of dilation at the origin.
b) The scale factor is \(\frac{1}{2}\)