who knows how to do geometry?

First draw the picture on a graph.

Then, there's a couple of things that you can do:

   Since it says add 5 to each x-value and subtract 2 from each y-value;

    ---   For each corner point, find a new corner point 5 spaces to the right and 2 spaces down, then                                    connect these points to get the new picture.

    or you can:

    ---   For each corner point, take the x-value and add 5, take the y-value and subtract 2, then graph these                         points and draw the new picture.

Either way, you should get the same new picture (this new picture is the image).

What's teh question?

the question is how do you translate a figure in the coordinate plane

If your original function is  y  =  x²

and you want to translate it 3 units to the right, replace  x  with  x - 3:  y  =  (x - 3)².

If you want ot translate it 5 units to the left, replace  x  with  x + 5:  y  =  (x + 3)².

Notice, if you want to move it to the right, use a - sign; to the left, use a + sign.

If you want to translate it 4 units up, replace  y  with  y - 4:  y - 4  =  x²

                (or y = x² + 4).

If you wnat to translate it 7 units down, replace  y  with  y + 7:  y + 7  =  x²  

                (or y = x² - 7).

A translation of the vertex from (0, 0) to (a, b) results in the equation:  y - b  =  (x - a)².

butdont you have to subtract 2 from the y coordinates

Where did the 2 come from?

well in my book its says "first draw ABCD. find the translation of each vertex by adding 5 to its x coordinates and subtracting 2 from its y coordinates then draw ABCD and its image"