What is the image of (4,-8) after a dilation by a scale factor of 1/4 centered at the origin

What are the coordinates of the point is 1/4 of the way from a (-6, -3) to b (6, 1)? a. (-3, -2) b. (0, -2) c. (-1, 0) d. (3, 2)

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Which geometric principle is used to justify the construction below?