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

Question

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

Answer 1

Let (a, b) be the point

As we move along the line segment from (-4, 2) to (-1, -4), the x coordinate increases by 3 and the y-coordinate decreases by 6. We are dividing the line segment into 1+5 equal parts.

a = -4 + (1/6)(3) = -3.5 and b = 2 - (1/6)(6) = 1

So, (a, b) = (-3.5, 1)