Question

1. hikmat says that dilating a figure by a scale factor of \\( \frac { 3 } { 2 } \\) will produce an image that is smaller than the pre - image. is hikmats claim correct? explain your thinking.

Explanation:

Step1: Understand the effect of scale factor

If the scale factor \(k\) of a dilation satisfies \(0 < k< 1\), the image is smaller than the pre - image. If \(k = 1\), the image is congruent to the pre - image. If \(k>1\), the image is larger than the pre - image.

Step2: Analyze the given scale factor

Here, the scale factor \(k=\frac{3}{2}=1.5\). Since \(1.5>1\).

Answer:

Hikmat's claim is incorrect. When the scale factor of a dilation is \(\frac{3}{2}\) (or \(1.5\)), since \(1.5 > 1\), the image produced by the dilation will be larger than the pre - image.