Question

for exercises 9 and 10, use the graph.

1. what transformation maps triangle qrs to triangle qrs? (lesson 5)
2. complete the proportions. then determine whether △qrs is similar to △qrs. (lesson 6)

\\(\frac{rs}{qr}=\frac{5}{2}\\) \\(\frac{rs}{qr}=\frac{3}{1}\\)

Explanation:

Step1: Analyze the transformation visually

By observing the graph, we can see that triangle QRS and triangle Q'R'S' have the same shape and orientation, but different positions. The transformation that moves a figure without changing its shape, size, or orientation is a translation.

Step2: Determine the translation rule

Count the number of units the vertices of triangle QRS have moved to get to the vertices of triangle Q'R'S'. We can see that each point of triangle QRS has moved 3 units to the right and 4 units down.

Step3: Check similarity for question 10

For two triangles to be similar, the ratios of their corresponding sides must be equal.
Let's assume the length of QR = 2 units and RS = 5 units for triangle QRS. For triangle Q'R'S', if we assume Q'R' = 1 unit and R'S' = 3 units.
The ratio of corresponding sides: $\frac{RS}{QR}=\frac{5}{2}$ and $\frac{R'S'}{Q'R'}=\frac{3}{1}$. Since $\frac{5}{2}
eq\frac{3}{1}$, $\triangle Q'R'S'$ is not similar to $\triangle QRS$.

Answer:

1. The transformation is a translation 3 units to the right and 4 units down.
2. $\frac{R'S'}{Q'R'}=\frac{3}{1}$, $\triangle Q'R'S'$ is not similar to $\triangle QRS$.