Question

figure ( j k l m ) is dilated by a scale factor of ( \frac { 1 } { 2 } ) to form its image, figure ( j ^ { prime } k ^ { prime } l ^ { prime } m ^ { prime } ).
when the scale factor is less than 1, the
image is closer to the center of dilation.
which figure is larger?
the original figure
the dilated image

Explanation:

Step1: Understand the effect of dilation

Dilation is a transformation that changes the size of a figure. When the scale factor \(k\) is between \(0\) and \(1\) (\(0 < k<1\)), the image of the dilation is smaller than the original figure. Here, the scale factor \(k = \frac{1}{2}\), and \(0<\frac{1}{2}<1\).

Step2: Compare the original and dilated figure

Let the side - length of the original figure \(JKLM\) be \(s\). After dilation, the side - length of the dilated figure \(J'K'L'M'\) is \(s\times k\). Substituting \(k=\frac{1}{2}\), the side - length of the dilated figure is \(\frac{1}{2}s\). Since \(\frac{1}{2}s

Answer:

the original figure