Question

The point is first rotated clockwise about the origin, translated 6 units to the left, and then reflected across the line .Write a function S to represent the sequence of transformations applied to the point .

Answer 1

we have that

First

Rotate 180 degrees clockwise about the origin

the rule is

S(x,y) --------> S'(-x,-y)

Second

translated 6 units to the left

the rule is

S'(-x,-y) -----> S''(-x-6,-y)

Third

Reflect across the line y=x

the rule is

the x-coordinate and y-coordinate change places

S''(-x-6,-y) ------> S''''(-y,-x-6)

therefore

the final answer is (-y,-x-6)