Question

Items 2. Find the coordinates of thevertices of each image.

Answer 1

We need to find the following operation

`T_((-1,2))\circ R_(x-axis)(QRST)`

which means that we need to find first the reflection over the x-axis of the figure QRST:

`R_(x-axis)(QRST)`

and then translate the result 1 unit left and 2 units up:

`T_((-1,2))`

In this regard, the rule for a reflection over the x-axis is given by

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

Then, by applying the reflection rule, we have that

`\begin{gathered} Q(1,3)\longrightarrow Q^(\prime)(1,-3) \\ R(3,-3)\longrightarrow R^(\prime)(3,3) \\ S(0,-2)\longrightarrow S^(\prime)(0,2) \\ T(-2,1)\longrightarrow T^(\prime)(-2,-1) \end{gathered}`

Now, the translation rule for 1 units to the left and 2 units up

`(x,y)\longrightarrow(x-1,\text{ y+2)}`

Then, by applyin this rule to the last result, we have

`Q^(\prime)(1,-3)\longrightarrow Q´´(1-1,-3+2)=Q´´(0,-1)`

and

`R^(\prime)(3,3)\longrightarrow R´´(3-1,3+2)=R´´(2,5)`

and

`S^(\prime)(0,2)\longrightarrow S´´(0-1,2+2)=S´´^{}(-1,4)`

and finally,

`T^(\prime)(-2,-1)\longrightarrow T´´^{}(-2-1,-1+2)=T´´(-3,1)`

Therefore, the answer is:

`\begin{gathered} Q´´(0,-1) \\ R´´(2,5) \\ S´´^{}(-1,4) \\ T´´(-3,1) \end{gathered}`