Question

triangle dog is the image that resulted from a dilation of triangle cat. the center of dilation is the point. the scale factor is

Explanation:

Step1: Identify center of dilation

The center of dilation is the point that stays fixed during the dilation. By observing the graph, we can see that the lines connecting corresponding points (e.g., C - D, A - O, T - G) intersect at the origin (0,0). So the center of dilation is (0,0).

Step2: Calculate scale factor

We can use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or simply count the grid - units for corresponding line segments. Let's consider the line segment CA and DO. The length of CA: \(C(-6,5)\), \(A(2,1)\), \(d_{CA}=\sqrt{(2 + 6)^2+(1 - 5)^2}=\sqrt{64 + 16}=\sqrt{80}=4\sqrt{5}\). The length of DO: \(D(- 3,2.5)\), \(O(1,0.5)\), \(d_{DO}=\sqrt{(1+3)^2+(0.5 - 2.5)^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\). The ratio of the lengths of DO to CA is \(\frac{d_{DO}}{d_{CA}}=\frac{2\sqrt{5}}{4\sqrt{5}}=\frac{1}{2}\). So the scale factor is \(\frac{1}{2}\).

Answer:

The center of dilation is (0,0).
The scale factor is \(\frac{1}{2}\).