How do you find x so distance between the points (6, -1) and (x, 9) is 12?

1 Answer
Jun 12, 2016

Problems like this require the involvement of the distance formula, d = sqrt((x_ 2 - x_1)^2 + (y_2 - y_1)^2)

Explanation:

d = sqrt((x_ 2 - x_1)^2 + (y_2 - y_1)^2)

12 = sqrt((x - 6)^2 + (9 - (-1))^2)

12 = sqrt(x^2 - 12x + 36+ 100)

12 = sqrt(x^2 - 12x + 136

(12)^2 = (sqrt(x^2 - 12x + 136))^2

144 = x^2 - 12x + 136

0 = x^2 - 12x - 8

By the completion of square method:

0 = 1(x^2 - 12x + n) - 8

n = (b/2)^2

n = (-12/2)^2

n = 36

0 = 1(x^2 - 12x + 36 - 36) - 8

0 = 1(x^2 - 12x + 36) - 36 - 8

0 = 1(x - 6)^2 - 44

44 = (x - 6)^2

+-sqrt(44) = x - 6

+-sqrt(44) + 6 = x

+-2sqrt(11) + 6 = x

x = 2(3 - sqrt(11)) or 2(3 + sqrt(11))

Checking back in the original equation, you will find both solutions work.

Hopefully this helps!

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