Question

what is the image point of A(4,2) after the composition of transformations defined by reflection over the line y=x and rotation of 90 degrees?

Answer 1

Answer: If you are graphing (4,2), that would be in Quadrant one, so if you wanted a reflection of this and it is turned 90 degrees, guessing it would be in Quadrant three, points of (-4,-2).

Hope this is right and I hope this helps you out. ☺

Answer 2

Transformation involves changing the position of a point.

The image of A is (-4,2)

Point A is given as:

$\mathbf{A = (4,2)}$

The rule of reflection over line y = x is:

$\mathbf{(x,y) \to (y,x)}$

So, we have:

$\mathbf{A'= (2,4)}$

The rule of rotation of 90 degrees

$\mathbf{(x,y)\to(-y,x)}$

So, we have:

$\mathbf{A" = (-4,2)}$

Hence, the image of A is (-4,2)

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