Distance formula: The distance between points [tex]$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$[/tex] and [tex]$\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$[/tex] is given by [tex]$\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$[/tex]
So, we have
[tex]&\sqrt{(2-6)^{2}+(6+2)^{2}} \\[/tex]
[tex]$(2-6)^{2}+(6+2)^{2}=80$[/tex]
[tex]$=\sqrt{80}$[/tex]
Prime factorization of [tex]$80: 2^{4} \cdot 5$[/tex]
[tex]$=\sqrt{2^{4} \cdot 5}$[/tex]
Apply radical rule: [tex]$\sqrt{a b}=\sqrt{a} \sqrt{b}$[/tex]
[tex]$\sqrt{2^{4} \cdot 5}=\sqrt{2^{4}} \sqrt{5}$[/tex]
[tex]$=\sqrt{2^{4}} \sqrt{5}$[/tex]
[tex]$\sqrt{2^{4}}=4$[/tex]
[tex]$=4 \sqrt{5}$[/tex]
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in any direction. A ray has just one endpoint and an endlessly long other ends, as opposed to a line segment that has two endpoints.
In a line, a line segment has two distinct ends. The line segment's length, which is the separation of two fixed points, is constant. The length can be calculated in feet or inches, or in metric measurements like centimeters (cm) or millimeters (mm).
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