Question

The point below will be reflected over the line y = x and then translated two units left and one unit up.5421-5-4-3-2-10234-1-2-3-4-5What are the coordinates of the point after this sequence of transformations?

Answer 1

A reflection over the line y=x implies exchanging the x and y coordinates of a point. For example if you take a generic point (a,b) then its reflection over y=x is (b,a). Our point is (-1,3) so its reflection over y=x is the point (3,-1).

Then we have to translate it two units left. Translating a point left means that we are moving towards negative x values so we need to substract 2 from the x coordinate:

$(3,-1)\rightarrow(3-2,-1)=(1,-1)$

Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:

$(1,-1)\rightarrow(1,-1+1)=(1,0)$

And these are the final coordinates. In the following picture you have the points you get after each step (from A to D) with the y=x line in blue: