Question

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the shadow represented by figure hijkchanges to form figure hijk.
how do the figures compare?
figure hijk a dilationof figure hijk.
the figures similar.

Explanation:

Step1: Understand dilation

Dilation is a transformation that enlarges or reduces a figure by a scale factor with respect to a center point. In the given figure, we can observe that the lines connecting corresponding vertices (e.g., \(H\) to \(H'\), \(I\) to \(I'\), \(J\) to \(J'\), \(K\) to \(K'\)) pass through a common center point. This is a key characteristic of dilation.

Step2: Check similarity

Similar figures have the same shape but not necessarily the same size. For two figures related by dilation, the corresponding angles are equal (since dilation is a similarity transformation). The ratio of the lengths of corresponding sides is constant (equal to the scale factor).

Answer:

Figure \(H'I'J'K'\) is a dilation of figure \(HIJK\). The figures are similar.