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what is m if distance between points (2,m),(m,-2) is 4?

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foxxalyn | Student, College Freshman | eNoter

Posted August 24, 2013 at 3:49 PM via web

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what is m if distance between points (2,m),(m,-2) is 4?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 24, 2013 at 4:07 PM (Answer #1)

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You should use the following distance formula, such that:

`D = sqrt((x_B - x_A)^2 + (y_B - y_A)^2)`

Considering `A(2,m)` and `B(m,-2)` yields:

`D = sqrt((m - 2)^2 + (-2 - m)^2)`

`D = sqrt((m - 2)^2 + (-(2 + m))^2)`

`D = sqrt((m - 2)^2 + (2 + m)^2)`

Since the problem provides the information that the distance between the points A and B is 4, yields:

`4 = sqrt((m - 2)^2 + (2 + m)^2)`

Squaring both sides, yields:

`16 = (m - 2)^2 + (m + 2)^2`

Expanding the squares, yields:

`16 = m^2 - 4m + 4 + m^2 + 4m + 4`

Reducing duplicate terms yields:

`16 = 2m^2 + 8 => 2m^2 = 8 => m^2 = 4 => m = +-2`

Hence, evaluating the values of coordinates m, under the given conditions, yields `m = +-2.`

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