Consider the figure at the right. if ️xyz is translated using the vector (x, y) --> (x-3,y+3) , then rotated 180 degrees about the origin, what will be the x-coordinate of z'?

Given coordinate of Z of the given figure (-1,-1).

First triangle XYZ is being translated by the rule (x,y) --> (x-3, y+3).

On applying that rule, the new coordinates of Z would be

(-1,-1)  >  (-1-3 , -1+3) = (-4, 2).

Now, we need to apply rotation 180 degrees about the origin.

The rule for rotation 180 degrees about the origin is (x,y) --> (-x,-y).

Therefore, final coordinate of Z after rotation 180 degrees about the origin would be

(-4, 2) ---> (4, -2).

good job you smart son of a gun you are smarter that einstein. 7