Question

problem 6
the diagrams shows a pair of similar figures, one contained in the other. name a point and a scale factor for a dilation that moves the larger figure to the smaller one.

Explanation:

Step1: Identify center of dilation

The two figures share point \(A(0,0)\), so this is the center.

Step2: Compare corresponding side lengths

Length of \(AD = 3 - 0 = 3\), length of \(AB = 1 - 0 = 1\). Scale factor is \(\frac{\text{smaller length}}{\text{larger length}}\).
<Expression>
$\text{Scale factor} = \frac{AB}{AD} = \frac{1}{3}$
</Expression>

Answer:

Center of dilation: Point \(A(0,0)\), Scale factor: $\frac{1}{3}$