Question

What are the coordinates of the point on the directed line segment from

(-6, 7) to (9, -5) that partitions the segment into a ratio of 5 to 1?

Answer 1

(6.5, -3)

Explanation:

You want the coordinates of a point P that will divide the segment from A(-6, 7) to B(9, -5) into the ratio 5:1.

Weighted average

A weighted average is the sum of products of values and their weights, divided by the total of the weights.

In this case, we want the weighted average of the coordinates of points A and B, using the first segment length as the weight of the second point, and vice versa:

P = (5B +1A)/(5+1)

Solution

P = (5(9, -5) +(-6, 7))/6 = (45-6, -25+7)/6 = (39, -18)/6

P = (6.5, -3)

The point that divides the segment in ratio 5:1 is (6.5, -3).