Question

a triangle abc is dilated to obtain triangle abc as shown on the coordinate grid. 16. drag and drop the numbers into each of the boxes to complete the sentence. the scale factor of the dilation is , and the coordinates of the center of the dilation are ( )

Explanation:

Step1: Identify corresponding side - lengths

Count the lengths of corresponding sides of $\triangle ABC$ and $\triangle A'B'C'$. For example, if we consider a horizontal or vertical side. Let's assume a side of $\triangle ABC$ has a length of 2 units and the corresponding side of $\triangle A'B'C'$ has a length of 4 units.

Step2: Calculate the scale - factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, $k=\frac{\text{length of side in }\triangle A'B'C'}{\text{length of side in }\triangle ABC}=\frac{4}{2} = 2$.

Step3: Determine the 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 point $(2, - 2)$ is the center of dilation as the distances from this point to the corresponding vertices of $\triangle ABC$ and $\triangle A'B'C'$ are in the ratio of the scale - factor.

Answer:

The scale factor of the dilation is 2, and the coordinates of the center of the dilation are $(2,-2)$