Question

the blue figure is a dilation of the red figure. identify the type of dilation and find the scale factor. the dilation is the scale factor is a reduction an enlargement 1/2 1/4 3/2 3 2 3/4 2/3

Explanation:

Step1: Observe figure size

The blue figure is smaller than the red figure, so it is a reduction.

Step2: Select corresponding side

Let's consider the horizontal side of the red - figure from \(Y\) to \(Z\). The length of the horizontal side of the red - figure from \(Y\) to \(Z\) is \(4\) units (from \(x=- 3\) to \(x = 1\)). The length of the corresponding horizontal side of the blue - figure is \(2\) units (from \(x=-1\) to \(x = 1\)).

Step3: Calculate scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the image to the length of the corresponding side of the pre - image. So \(k=\frac{\text{length of side of image}}{\text{length of corresponding side of pre - image}}=\frac{2}{4}=\frac{1}{2}\).

Answer:

The dilation is a reduction.
The scale factor is \(\frac{1}{2}\)