Question

Given A(-1,10) and B(x,2). Find the value(s) of x if AB = 10.

Answer 1

Answer:

$x=5 \ and \ x=-7$

Step-by-step explanation:

We apply distance formula to find length of AB.

Distance formula:

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

$A(-1,10)\textrm{ } B(x,2)\\\textrm{Length of AB=} \sqrt{(x-(-1))^2+(2-10)^2}=\sqrt{(x+1)^2+(-8)^2}=\sqrt{(x+1)^2+64}\\\textrm{Length of AB=}10\\\sqrt{(x+1)^2+64}=10\\ \textrm{Squaring both sides}\\\\(\sqrt{(x+1)^2+64 })^2=10^2\\ (x+1)^2+64=100\\\textrm{Subtracting both sides by 64}\\(x+1)^2+64-64=100-64\\(x+1)^2=36\\\textrm{Taking square root both [tex]sides}\\\sqrt{(x+1)^2}=\sqrt{36} \\ x+1=\pm6\\\textrm{Subtracting both sides by 1}\\x+1-1=\pm6-1$

$x=6-1=5\\x=5\\\textrm{and }\\x=-6-1=-7\\x=-7$

$\therefore\textrm{ } x=5\ and \x=-7$