Look at the figure drawn on the coordinate plane and write down the X and Y coordinates for each vertex, or corner, of the shape. For instance, the corners of a triangle might be (1,-3), (2,5), and (-9,4).
Multiply the X-coordinate of each point by the scale factor. Then, do the same with each Y-coordinate. For instance, if the scale factor was 4, you would multiply -1 and -3 both by 4 to get a new point of (-4, -12). Your three original points would become (-4, -12), (8, 20), and (-36, 16).
Plot the new points as vertices on the coordinate plane. Then, use a ruler or straight edge to connect the dots and create the new figure.