Question

Answer the questions by drawing on the coordinate plane below. You may need to print the test and graphthe images by hand.

Answer 1

From the figure, we have the following coordinates of the vertices :

`\begin{gathered} Q(-4,2) \\ R(-1,1) \\ S(-2,4) \end{gathered}`

a. Rotation of 180 degrees about the origin has a rule of :

`(x,y)\rightarrow(-x,-y)`

The sign of the coordinates will change from positive to negative or negative to positive.

The new coordinates will be :

`\begin{gathered} Q(-4,2)\rightarrow Q^(\prime)(4,-2) \\ R(-1,1)\rightarrow R^(\prime)(1,-1) \\ S(-2,4)\rightarrow S^(\prime)(2,-4) \end{gathered}`

The graph will be :

b. Reflection across the x-axis has a rule of :

`(x,y)\rightarrow(x,-y)`

Only the y coordinate will change its sign.

So from the coordinates we got in a.

`\begin{gathered} Q^(\prime)(4,-2)\rightarrow Q^(\doubleprime)(4,2) \\ R^(\prime)(1,-1)\rightarrow R^(\doubleprime)^(\prime)(1,1) \\ S^(\prime)(2,-4)\rightarrow S^(\doubleprime)(2,4) \end{gathered}`

The graph will be :