what are the coordinates of point c on the directed segment from A(-4,9) to B(-5,-9) that partitions the segment such that AC:CB is 5:4?

Question

what are the coordinates of point c on the directed segment from A(-4,9) to B(-5,-9) that partitions the segment such that AC:CB is 5:4?

choices

(-0.6,-5)

(-4.6,-1)

(-6.6,1)

(-1.6,2)

Answer 1

Since the x value of the endpoints are -5 and -4, C must have an x value between the two. The only one of the possible choices that fits is (-4.6, -1)

For a more sophisticated method:

Since the ratio of change is 5:4 and amounts of change are -1 and -18, x_c = -4 - (1* 5/9) = -4 5/9, which is roughly -4.6, and y_c is 9 - (18 * 5/9) which is -1 indicating (-4.6, -1) is the location of C

Answer 2

Since the ratio is 5:4, the x coordinate of point c is 5/9 of the way between the x coordinates of points A and B: -4 and -5, which is -4.55, which rounds to -4.6, and the y coordinate of point c is 5/9 of the way between the y coordinates of A and B: 9 and -9 which is -1. So the answer is (-4.6,-1).