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# need help with coordinates

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Given RT below, if S lies on RT such that theratio of RS to ST is 3:1, find the coordinates
of S. Sep 14, 2020

It would be (-2, -3). First, we use the distance formula to find the distance between the two endpoints. $$\sqrt{(-5 + 1)^2+(3 + 5)^2} = 4\sqrt{5}$$ Since the line segment's length is $$4\sqrt{5}$$, we know the distance from R to S is $$3\sqrt{5}$$ as there is a 3:1 ratio in the line. Now to find the coordinates of point S. We can use Pythogorean Theorem to help solve this. In this case, $$3\sqrt{5}$$ is the hypotenuse. Squaring it gives 45, meaning the two legs' sum must be 45. Using perfect squares and some trial and error, we find the two legs are lengths 6 and 3. It will not be 6 units to the right, 3 units down as that would not be close to on the line. Which only leaves, 6 units down and 3 units to the right. Starting from the coordinates of R, which are (-5, 3), going 6 units down and 3 units to the right gives us the coordinate point (-2, -3).