What is the distance between $(8, 5)$ $(8,5)$ and $(1, 2)$ $(1,2)$ ?

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What is the distance between $(8, 5)$ $(8,5)$ and $(1, 2)$ $(1,2)$ ?

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Answer 1 · 2016-01-03T02:15:39

$distance = \sqrt{58}$ $"distance"=sqrt(58)$

Explanation:

We can find this distance using Pythagoras' formula. But now we only have one side of the triangle, so, we need to complete the rectangle triangle, and in order to make a $\frac{π}{2}$ $pi/2$ angle, we have to create two lines, one with the projection of the extremes in $x$ $x$ axis, and the other with the projections in $y$ $y$ axis. Then, we take the difference between the lines of both projections:
$△ x = 8 - 1 = 7$ $trianglex = 8-1 = 7$
$△ y = 5 - 2 = 3$ $triangley = 5-2 = 3$

Now, apply the formula: ${distance}^{2} = 7^{2} + 3^{2}$ $"distance"^2 = 7^2 + 3^2$
$distance = \sqrt{58}$ $"distance"=sqrt(58)$

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What is the distance between $(8, 5)$ $(8,5)$ and $(1, 2)$ $(1,2)$ ?

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