What are the coordinates of the point 2/3 of the way from A (-1,7) to B (5,1)

Answer 1

The horizontal distance from A to B is given by 5 - (-1) = 6. We want to start at -1 and move 2/3 of that distance.

So the x-coordinate of the target point is -1 + 2/3(6) = -1 + 4 = 3.

In a similar fashion the y coordinate of the target point is found by:

7 + 2/3 (1 - 7) = 7 + 2/3(-6) = 7 + (-4) = 3.

So the point 2/3 of the way from A to B is (3,3).

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In general if the starting point is given by (x₁, y₁), the ending point by (x₂,y₂) and k is the fraction of the distance from point 1 to point 2; the target point is given by:

(x₁+k(x₂-x₁), y₁+k(y₂-y₁))