# Summary of Transformation Rules

Several of you have requested a summary of all the transformation rules…

Here you go! You may want to rewrite some of them to make more sense to you. I’ve also made these available as a Quizlet deck.

Translate a units right/left and b units up/down
$(x,y)\to (x+a,y+b)$

Reflect across the x-axis
$(x,y)\to (-x,y)$

Reflect across the y-axis
$(x,y)\to (x,-y)$

Rotate 90º clockwise about the origin
$(x,y)\to (y,-x)$

Rotate 90º counter-clockwise about the origin
$(x,y)\to (-y,x)$

$(x,y)\to (-x,-y)$
Dilation centered on the origin, scale factor of $k,\ k>0$
$(x,y)\to (kx,ky)$
You’ve also learned through your homework that a reflection across the line $y=x$ looks like
$(x,y)\to (y,x)$