Question

Hey guys! I need a little help and this is a geometry question. What is the image of (8,7) under the reflection of across the line y= -x ?
I would guess (-7, 8).
The CORRECT answer is (-7, -8), but how??

Answer 1

Hmm... well reflection around the y = x line would be
1 0
0 1 << using this transformation matrix

x = 1 * 8 + 0 * 7 = 8 + 0 = 8
y = 0 * 8 + 1 * 7 = 0 + 7 = 7

So how do you go about doing a reflection about a y = -x line..?
i
the two arrows would be the vectors i and j, adding them together gets a vector on y = x that's how i got
1 0
0 1

so doing the same thing but for y = -x instead...

we're going to the right still, but instead we're going down!
1 0
0 -1

The reflection would then be
x: 1 * 8 + 0*7 = 8
y: 0 * 8 + -1*7 = -7
so instead, i get an (8,-7) out of this.

Now, I did all of this perhaps because I misunderstood the question, waah!
But...

How did you make your guess???