Question

Find the coordinates of a point on the directed segment from (-3,6) to (7,1) that divides it into a ratio of 3:1.

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Answer 1

Explanation:

To divide a directed segment, we need to divide the length of the segment, along the x and the y directions separately. Then add the subdivided segment to the starting point of the directed segment (-3,6) to get the point of division.

Let the length be denoted by delta, then

delta = (7,1) - (-3,6) = (10,-5)

Multiply delta by the ratio of 3 / (3+1) = 3/4

(10,-5) * 3/4 = (7.5, -3.75)

Add the subdivided segment to the starting point:

(-3,6) + (7.5, -3.75) = (4.5, 2.25)

So the point of division is (4.5, 2.25)