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

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