Question

If the distance between two points P(x, 2) and Q(3,-6) is 10 units, find the value of x

Answer 1

distance between PandQ is 9

Answer 2

The value of x is 9 or -3

Step-by-step explanation:

$P=(x_1,y_1)=(x,2)\\Q=(x_2,y_2)=(3,-6)$

The distance between two points P(x, 2) and Q(3,-6) is 10 units

Formula : $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\\10= \sqrt{(3-x)^2+(-6-2)^2}\\100=(3-x)^2+64\\100-64=9+x^2-6x\\36=9+x^2-6x\\x^2-6x-27=0\\x^2+3x-9x-27=0\\x(x+3)-9(x+3)=0\\(x-9)(x+3)=0$

x=9,-3

Hence the value of x is 9 or -3

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