Question

Use the figure below to answer the questions.

Describe a sequence of transformations that maps ABC to A'B'C'

Answer 1

The transformation is a reflection in the line
`y=x` followed by a reflection in the line
`x=1` .

The mapping for a reflection in the line
`y=x` is
`(x,y) \rightarrow (y,x)` .

That is simply swapping the coordinates.


`A(-3,4) \rightarrow (4,-3)`


`B(-3,0) \rightarrow (0,3)`


`C(-1,3) \rightarrow (3,-1)`

Now we reflect the resulting coordinates in the line
`x=1` which has the mapping
`(x,y) \rightarrow (2(1)-x,y)`

So we transform the resulting coordinates as follows:


`(4,-3) \rightarrow A'(2(1)-4,-3)`


`(0,-3) \rightarrow B'(2(1)-0,-3)`


`(3,-1) \rightarrow C'(2(1)-3,-1)`

Hence we have


`A'(-2,-3),B'(2,-3) \: and\: C'(-1,-1)`