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what are the coordinates of the point on the directed line segment from (1,5) to (6,10) that portions the segment into a ratio of 3 to 2?

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2 votes

Answer:

The answer is point (4,8)

Explanation:

The horizontal (x) distance between the given points is 6-1 = 5.

If the horizontal distance is 5, then because the ratio of the given points is 3 to 2, we can say that 3/5 of 5 is 3. The horizontal distance between (1,5) and (x,y) is 3, so x = 4.

We can do the same with the vertical (y) distance, which is 10-5 = 5.

Again, 3/5 of 5 is 3, so y = 5+3 = 8

Answer: the point is (4,8).

CHECK: We can check this result by finding the distances between the given points to (4,8), and calculating the distance.

Distance between (1,5) and (4,8) = √18 = 3√2

Distance between (6,10) and (4,8) = √8 = 2√2

The ratio between the distances is 3:2, so the solution checks out.

User DanielBarbarian
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