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Distance between two points

In this article we review calculating the distance between two points, when coordinates of these points are known.

Distance between two plane points $A(x_1;y_1)$ and $B(x_2;y_2)$ can be calculated with this formula: $${AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$$

Example No. 1
What is the distance between two plane points $A(5;10)$ and $B(20;30)$?

Using the formula above, we get:

$${AB=\sqrt{(20-5)^2+(30-10)^2}=25}$$

Example No. 2
What is the missing coordinate $A(x;7)$ value x, if we have other point $B(2;3)$ and the length of segment $AB$ is 5?

Using the formula above, we get this equation:

$${\sqrt{(2-x)^2+(3-7)^2}=5}$$

To solve this equation, we take a square above sides of the equation, then simplify everything and solve equation by factoring:

\begin{align} \Bigl(\sqrt{(2-x)^2+(3-7)^2}\Bigr)^2 & =5^2 \\ (2-x)^2+16 & =25 \\ 4-4x+x^2+16 & =25 \\ x^2-4x-5 & =0 \\ (x-5)(x+1) & =0 \\ x=5 & \ \text{or} \ x=-1 \\ \end{align}

Answer: x = 5 or x = -1

2019-03-02

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