Question

Use the distance formula to find the distance between the points given.

Answer 1

The distance between the points is $4\sqrt{13}$

Step-by-step explanation:

The formula of the distance between two points $(x_{1},y_{1})$ and

$(x_{2},y_{2})$ is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

To find the distance between two point:

• Put one of the two point as $(x_{1},y_{1})$
• Put the other point as $(x_{2},y_{2})$
• Substitute then in the rule of the distance and calculate the distance

∵ The two points are (18 , -2) and (6 , -10)

- Put (18 , -2) as $(x_{1},y_{1})$ and (6 , -10) as $(x_{2},y_{2})$

∴ $x_{1}$ = 18 and $x_{2}$ = 6

∴ $y_{1}$ = -2 and $y_{2}$ = -10

- Substitute them in the rule below

∵ $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∴ $d=\sqrt{(6-18)^{2}+(-10--2)^{2}}$

∴ $d=\sqrt{(-12)^{2}+(-10+2)^{2}}$

∴ $d=\sqrt{(-12)^{2}+(-8)^{2}}$

∵ (-12)² = 144 and (-8)² = 64

∴ $d=\sqrt{144+64}$

∴ $d=\sqrt{208}$

∵ $\sqrt{208}=4\sqrt{13}$

∴ $d=4\sqrt{13}$

The distance between the points is $4\sqrt{13}$

Learn more:

You can learn more about the distance between two points in brainly.com/question/3969582

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