Mario says that are reflecting a point XY across the y axis and then dilating the reflection images by r will produce the same final image as dilating the point by r first and the reflecting the dilation image across the y axis. Use coordinate notation to show Mario is correct

Answer 1

matrix for reflection over y axis:
-1 +0
+0 +1

dilation matrix
r r
or
r
r

matrix multiplication is not necessarily comutative

dilate first
r r
* x y = r x, r y
then reflect
rx , ry
*
-1 +0
+0 +1
= -rx , ry

now reflect first
-1 +0 |x|
+0 +1 |y|

= -x , + y
now dilate
-rx , + r y
seems to be the same

Answer 2

Thank you