Question

Trapezoid ABCD is reflected over the line y = x. What rule shows the input and output of the reflection, and what is the new coordinate of A'?

Answer 1

(x,y)→(y,-x); A' is at (1, 5)
(x,y)→(y,x); A' is at (1, -5)
(x,y)→(-x,y); A' is at (5, 1)
(x,y)→(-x,-y); A' is at (5, -1)

Answer 2

@mathmate

Answer 3

It is always a good idea to retrace the transformations.
The question states that A has undergone the transoformation
(x,y)->(y,-x) which results in (1,5)
We need to do the inverse transformation, namely find (x,y).
From the above, y=1 and -x=5 which means that x=-5, y=1, A(-5,1)
Now you need to choose the transformation of reflection about y=x.

Hints:
\(S_{y=x}: (x,y) -> (y,x)\) ..........reflection about y=x
\(S_{y=-x}: (x,y) -> (-y,-x)\).........reflection about y=-x