How do you find the distance and midpoint between the two points. (4, -6) (-2, 8)?

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How do you find the distance and midpoint between the two points. (4, -6) (-2, 8)?

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Answer 1 · 2015-10-16T11:19:40

$d = 2sqrt(58)$
$M = (1,1)$

Explanation:

To find the distance we just apply Pythagoras. Think of it this way:

The difference between the $x$ points causes a straight horizontal line, the difference between the $y$ points causes a straight vertical line, so the distance between the two points is the hypotenuse, or

$d^2 = Deltax^2 + Deltay^2$

$d = sqrt(Deltax^2 + Deltay^2)$

$d = sqrt((-2-4)^2 + (8-(-6))^2)$

$d = sqrt(36 + 196)$

$d = sqrt(232)$

$d = sqrt(58*4) = 2sqrt(58)$

The midpoint between two points, $M$ , is literally just the average between the $x$ values and the average between the $y$ values, or

$M = (bar x, bar y)$

We have that

$bar x = (4-2)/2 = 2/2 = 1$

And that

$bar y = (8 -6)/2 = 2/2 = 1$

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How do you find the distance and midpoint between the two points. (4, -6) (-2, 8)?

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Explanation:

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