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# Coordinates

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36
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The distance between the points (x,21) and (4,7) is 10sqrt(3) Find the sum of all possible values of x.

Jun 1, 2022

#1
+1750
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By the distance formula, we have the following equation: $$10 \sqrt 3 = \sqrt{{(x-4)}^2 + (21-7)^2}$$

Here's how to solve for x:

1 - Completely simplify the left-hand side

2 - Square both sides

3 - Subtract the left-hand side from both sides. This will now form a quadratic.

4 - Use Vieta's formula ($$-b \over a$$) to find the sum of the values of x.

Jun 1, 2022