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

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Answer 1 · 2016-06-12T00:46:35

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

#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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