Question #a99ba

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Answer 1 · 2017-10-11T03:16:15

The distance is $\sqrt{72}$ $\sqrt{72}$ units on the coordinate plane.

You can solve this using the Distance Formula, which is derived from the Pythagorean Theorem.

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

where $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ are two points.

In your question, we have:

$(x_{1}, y_{1}) = (- 4, 8)$ $(x_1,y_1)=(-4,8)$

and

$(x_{2}, y_{2}) = (2, 2)$ $(x_2,y_2)=(2,2)$

So, we can write the distance formula as:

$d = \sqrt{{(2 - (- 4))}^{2} + {(2 - 8)}^{2}}$ $d=\sqrt{(2-(-4))^2+(2-8)^2}$

$d = \sqrt{{(6)}^{2} + {(- 6)}^{2}}$ $d=\sqrt{(6)^2+(-6)^2}$

$d = \sqrt{36 + 36}$ $d=\sqrt{36+36}$

$d = \sqrt{72}$ $d=\sqrt{72}$

$\therefore$ the distance between $(-4,8)$ and $(2,2)$ is $\sqrt{72}$

Answer 2 · 2017-10-11T10:24:30

See a solution process below:

The formula for calculating the distance between two points is:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the values from the points in the problem gives:

$d = sqrt((color(red)(2) - color(blue)(-4))^2 + (color(red)(2) - color(blue)(8))^2)$

$d = sqrt((color(red)(2) + color(blue)(4))^2 + (color(red)(2) - color(blue)(8))^2)$

$d = sqrt(6^2 + (-6)^2)$

$d = sqrt(36 + 36)$

$d = sqrt(36 * 2)$

$d = sqrt(36)sqrt(2)$

$d = 6sqrt(2)$