How to find a point on a line in 3d given the distance from one of the points?

Let a line in three dimensions be specified by two points  and  lying on it, so a vector along the line is given by

To minimize the distance, set  and solve for  to obtain

where  denotes the dot product. The minimum distance can then be found by plugging  back into (2) to obtain

your answer is the last one

step-by-step explanation:

divide the length of a'c' by the length of ac to get a scale factor of two

& then reflect vertically (over the y-axis)

so your answer is dilation by a scale factor of 2 followed by reflection over the y-axis