What are the coordinates of the point on the directed line segment from (- 7, 2) to (- 4, - 10) that partitions the segment into a ratio of 5 to 1?

Answer 1

As we move along the line segment from (-7,2) to (-4,-10), the x-coordinate increases by 3 and the y-coordinate decreases by 12.

The point that we are looking for lies on the segment and is 5/6 of the way from (-7,2) to (-4,-10).

x-coordinate = -7 + (5/6)(3) = -4.5

y-coordinate = 2 - (5/6)(12) = -8

The point is (-4.5, -8).

Answer 2

Vector <3, - 12> is directed segment. Now let this point is (x, y). Then <x + 7, y - 2> = 5/6<3, - 12>

So, x + 7 = 5/2 and y - 2 = - 10; x = - 9/2, y = - 8. Point is (- 9/2, - 8)