Final answer:
To dilate a shape using (0,0) as the center of dilation and a scale factor of k=2, multiply each coordinate of the pre-image by the scale factor.
Step-by-step explanation:
To dilate a shape using (0,0) as the center of dilation and a scale factor of k=2, you multiply each coordinate of the pre-image by the scale factor.
For point A(4,2), the x-coordinate becomes 4*2=8 and the y-coordinate becomes 2*2=4.
So, the image of point A is (8,4).
Similarly, for point B(0,3), the x-coordinate remains the same since it is already 0 and the y-coordinate becomes 3*2=6.
So, the image of point B is (0,6).
For point C(1,-6), the x-coordinate becomes 1*2=2 and the y-coordinate becomes -6*2=-12.
So, the image of point C is (2,-12).