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Distance Formula

Find the valu...

Question

Find the value of $x$ such that $A B = B C$ where the coordinates of A, B and C are $(2, 1)$ , $(x, 0)$ and $(- 2, - 1)$ respectively.

A

1

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B

2

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C

- 2

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D

0

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Solution

The correct option is D $0$
Distance between two points $= \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
Given $A B = B C$
$\sqrt{(2 - x)^{2} + (1)^{2}} = \sqrt{(x + 2)^{2} + (1)^{2}}$
Squaring both sides
$(2 - x)^{2} + (1) = (x + 2)^{2} + (1)$
$4 + x^{2} - 4 x = x^{2} + 4 + 4 x$
$x = 0$

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