If the point A(x, 2) is equidistant from the points B(8, − 2) and C(2, − 2),


If the point A(x, 2) is equidistant from the points B(8, − 2) and C(2, − 2), find the value of x. Also, find the length of AB.


As per the question

$A B=A C$

$\Rightarrow \sqrt{(x-8)^{2}+(2+2)^{2}}=\sqrt{(x-2)^{2}+(2+2)^{2}}$

Squaring both sides, we get


$\Rightarrow x^{2}-16 x+64+16=x^{2}+4-4 x+16$

$\Rightarrow 16 x-4 x=64-4$

$\Rightarrow x=\frac{60}{12}=5$


$A B=\sqrt{(x-8)^{2}+(2+2)^{2}}$

$=\sqrt{(5-8)^{2}+(2+2)^{2}} \quad(\because x=2)$



Hence, x = 5 and AB = 5 units.

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