Question

if you know the pre - image coordinates, how can you find the image coordinates for any reflection or translation? use the examples if they help with your thinking. reflection: translation:

Explanation:

Step1: Reflection rules

For reflection over x - axis, if pre - image is $(x,y)$, image is $(x, - y)$. For reflection over y - axis, if pre - image is $(x,y)$, image is $(-x,y)$. For reflection over the line $y = x$, if pre - image is $(x,y)$, image is $(y,x)$.

Step2: Translation rules

If pre - image has coordinates $(x,y)$ and translation is $(a,b)$, then image coordinates are $(x + a,y + b)$.

Answer:

Reflection: For reflection over x - axis, change the sign of the y - coordinate. For reflection over y - axis, change the sign of the x - coordinate. For reflection over $y = x$, swap the x and y coordinates. Translation: Add the translation values to the pre - image coordinates.