Question

the vertices of PQR are P(-5,1), Q(-4,6), and R(-2,3), graph P"Q"R" after a composition of the transformations in the order they are listed.

Answer 1

We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).

In P(-5,1), x = -5 and y = 1

In Q(-4,6), x = -4 and y = 6 and

In R(-2,3), x = -2 and y = 3

`\begin{gathered} P(-5,\text{ 1) translates to (-5 -8, 1) }\rightarrow P^i(-13,\text{ 1)} \\ Q(-4,\text{ 6) translates to (-4 -8, 6) }\rightarrow Q^i(-12,\text{ 6)} \\ R(-2,\text{ 3) translates to (-2 -8, 3) }\rightarrow R^i(-10,\text{ 3)} \end{gathered}`

For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.

`\begin{gathered} At\text{ K = 2, }P^i(-13,\text{ 1) }\rightarrow\text{ }2(-13,\text{ 1) }\rightarrow\text{ }P^(ii)(-26,\text{ 2)} \\ Q^i(-12,\text{ 6) }\rightarrow\text{ }2(-12,\text{ 6) }\rightarrow\text{ Q}^(ii)(-24,\text{ 12)} \\ R^i(-10,\text{ 3) }\rightarrow\text{ }2(-10,\text{ 3) }\rightarrow\text{ R}^(ii)(-20,\text{ 6)} \end{gathered}`