Question

What are the coordinates of the point on the directed line segment from ( − 10 , 9 ) (−10,9) to ( − 4 , 3 ) (−4,3) that partitions the segment into a ratio of 1 to 5 help plss

Answer 1

(-9, 8)

Explanation:

You want the point that divides the segment from (-10, 9) to (-4, 3) into parts in the ratio 1:5.

Ratio

If the given segment's endpoints are named A and B, we want to find X such that AX : XB = 1 : 5.

The lengths can be written as the differences of the coordinates:

(X -A) : (B -X) = 1 : 5

Solution

Cross multiplying gives ...

5(X -A) = 1(B -X)

6X = B +5A

6X = (-4, 3) +5(-10, 9) = (-4-50, 3+45) = (-54, 48)

X = (-54, 48)/6 = (-9, 8)

The point that partitions the segment into a ratio of 1 to 5 is (-9, 8).

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