Question

find the image of (1,2) after a reflection about y = x followed by a reflection about y = -x. enter the number that belongs in the green box.

Explanation:

Step1: Reflect about \( y = x \)

When reflecting a point \((x,y)\) about the line \( y = x \), the transformation rule is \((x,y)\to(y,x)\).
For the point \((1,2)\), after reflection about \( y = x \), it becomes \((2,1)\).

Step2: Reflect the new - point about \( y=-x \)

When reflecting a point \((x,y)\) about the line \( y = -x \), the transformation rule is \((x,y)\to(-y,-x)\).
We have the point \((2,1)\) from the previous step. Applying the reflection rule about \( y=-x \):
Substitute \( x = 2\) and \( y = 1\) into \((-y,-x)\), we get \((-1,-2)\).

Answer:

\(-1\)