Question

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

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated by a scale - factor $k$ with the origin as the center of dilation, the new point is $(kx,ky)$. To find the scale - factor, we can compare the lengths of corresponding sides of the original and dilated triangles or the coordinates of corresponding points. Let's assume we can find the lengths of corresponding sides. If the length of a side of $\triangle STU$ is $l_1$ and the length of the corresponding side of $\triangle S'T'U'$ is $l_2$, then the scale - factor $k=\frac{l_2}{l_1}$.

Step2: Analyze the size relationship

If the dilated triangle $\triangle S'T'U'$ is smaller than the original triangle $\triangle STU$, the scale - factor $k$ is between $0$ and $1$. If $\triangle S'T'U'$ is larger than $\triangle STU$, $k>1$. If $\triangle S'T'U'$ and $\triangle STU$ are congruent, $k = 1$. Looking at the graph, we can see that $\triangle S'T'U'$ is smaller than $\triangle STU$. If we assume we can measure the lengths of corresponding sides (or use the coordinates of corresponding vertices), and find that the lengths of the sides of $\triangle S'T'U'$ are half of the lengths of the sides of $\triangle STU$. So the scale - factor $k=\frac{1}{2}$.

Answer:

A. Triangle STU is dilated by a scale factor of $\frac{1}{2}$ to create triangle S'T'U'