The distance between the points is [tex]4\sqrt{13}[/tex]
Step-by-step explanation:
The formula of the distance between two points [tex](x_{1},y_{1})[/tex] and
[tex](x_{2},y_{2})[/tex] is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
To find the distance between two point:
∵ The two points are (18 , -2) and (6 , -10)
- Put (18 , -2) as [tex](x_{1},y_{1})[/tex] and (6 , -10) as [tex](x_{2},y_{2})[/tex]
∴ [tex]x_{1}[/tex] = 18 and [tex]x_{2}[/tex] = 6
∴ [tex]y_{1}[/tex] = -2 and [tex]y_{2}[/tex] = -10
- Substitute them in the rule below
∵ [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∴ [tex]d=\sqrt{(6-18)^{2}+(-10--2)^{2}}[/tex]
∴ [tex]d=\sqrt{(-12)^{2}+(-10+2)^{2}}[/tex]
∴ [tex]d=\sqrt{(-12)^{2}+(-8)^{2}}[/tex]
∵ (-12)² = 144 and (-8)² = 64
∴ [tex]d=\sqrt{144+64}[/tex]
∴ [tex]d=\sqrt{208}[/tex]
∵ [tex]\sqrt{208}=4\sqrt{13}[/tex]
∴ [tex]d=4\sqrt{13}[/tex]
The distance between the points is [tex]4\sqrt{13}[/tex]
Learn more:
You can learn more about the distance between two points in brainly.com/question/3969582
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