How do you find all points that have an x -coordinate of –4 and whose distance from point (4, 2) is 10?

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Answer 1 · 2014-10-27T15:37:17

#D = root 2 ((x_1 - x_2)^2 + (y_1 - y_2)^2)#

We want #D = 10#

Let #(x_1, y_1)# be #(4, 2)#
Let #(x_2, y_2)# be #(-4, y_2)#

#10 = root 2 ((4 - (-4))^2 + (2 - y_2)^2)#

Squaring both sides we have

#(10 = root 2 ((4 - (-4))^2 + (2 - y_2)^2))^2#

#=> 100 = (4 - (-4))^2 + (2 - y_2)^2#

#=> 100 = (8^2) + (2 - y_2)^2#

#=> 100 = 64 + (4 - 4y_2 + (y_2)^2)#

#=> 36 = (y_2)^2 + 4y_2 + 4#

#=> (y_2)^2 + 4y_2 + 4 = 36#

#=> (y_2)^2 + 4y_2 - 32 = 0#

#=> (y_2 + 8)(y_2 - 4) = 0#

y_2 = -8, y_2 = 4