Question

5 triangle efg is dilated to create triangle efg using the origin as the center of dilation. which one of the following statements is true? a triangle efg is dilated by a scale factor of 1 to create triangle efg. b triangle efg is dilated by a scale factor of 2 to create triangle efg. c triangle efg is dilated by a scale factor of 4 to create triangle efg. d triangle efg is dilated by a scale factor of 3 to create triangle efg.

Explanation:

Step1: Identify corresponding points

Let's assume we can identify corresponding vertices of $\triangle EFG$ and $\triangle E'F'G'$ from the graph. For example, if a vertex of $\triangle EFG$ is $(x,y)$ and the corresponding vertex of $\triangle E'F'G'$ is $(x',y')$, the scale - factor $k$ of dilation with the origin as the center of dilation is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$).

Step2: Analyze side - length ratios

We can also compare the lengths of corresponding sides of the two triangles. If the length of a side of $\triangle EFG$ is $l_1$ and the length of the corresponding side of $\triangle E'F'G'$ is $l_2$, the scale - factor $k = \frac{l_2}{l_1}$. Suppose we find that if we measure the lengths of corresponding sides (using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for two - dimensional points), and we find that the lengths of the sides of $\triangle E'F'G'$ are twice the lengths of the sides of $\triangle EFG$.

Answer:

B. Triangle EFG is dilated by a scale factor of 2 to create triangle E'F'G'