MCQ
The point $P$ on $x -$axis equidistant from the points $A (-1,0)$ and $B (5,0)$ is
- ✓$(2,0)$
- B$(0,2)$
- C$(3,0)$
- D$(2,2)$
✓
Answer
Correct option: A.
$(2,0)$
$AP = BP$
$\Rightarrow AP ^2 = BP ^2$
$ A (-1,0) B (5,0) P (x, 0)$
$\text { Distance formula }=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
$\Rightarrow(-1-x)^2+(0-0)^2=(5-x)^2+(0-0)^2$
$\Rightarrow 1+x^2+2 x=25+x^2-10 x$
$\Rightarrow 12 x=24$
$\Rightarrow x=2$
$\therefore P =2,0$
$\Rightarrow AP ^2 = BP ^2$
$ A (-1,0) B (5,0) P (x, 0)$
$\text { Distance formula }=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
$\Rightarrow(-1-x)^2+(0-0)^2=(5-x)^2+(0-0)^2$
$\Rightarrow 1+x^2+2 x=25+x^2-10 x$
$\Rightarrow 12 x=24$
$\Rightarrow x=2$
$\therefore P =2,0$
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