Question

what type of transformation maps these two figures?

choose one written description and one algebraic description that maps the pre - image onto the image.

reflection over line ( y=-x )

reflection over the line ( y = x )

( (x,y)\to(-x,-y) )

( (x,y)\to(x + 2,y + 2) )

( (x,y)\to(-y,-x) )

( (x,y)\to(x + 4,y-4) )

( (x,y)\to(y,x) )

translation right and down

( (x,y)\to(-x,y) )

rotation 180 degrees around the origin

reflection over the y - axis

Explanation:

Step1: Recall reflection over \(y = x\) rule

The rule for reflection over the line \(y=x\) is \((x,y)\to(y,x)\).

Step2: Check a point

Take point \(C(-1,3)\). After reflection over \(y = x\), it should be \((3,-1)\) which is \(C'\).
Take point \(G(-1,3)\). After reflection over \(y = x\), it should be \((3,-1)\) which is \(G'\).

Answer:

Written description: Reflection over the line \(y = x\)
Algebraic description: \((x,y)\to(y,x)\)