MCQ
The point on $X -$axis which is equidistant from points $A (-1,0)$ and $B (5,0)$ is.
- A$(0,2)$
- ✓$(2,0)$
- C$(3,0)$
- D$(0,3)$
✓
Answer
Correct option: B.
$(2,0)$
Let the required point be $P ( x , 0)$.
Then, $(PA)^2=(PB)^2$
$\Rightarrow(x+1)^2=(x-5)^2$
$\Rightarrow x^2+2 x+1=x^2-10 x+25$
$\Rightarrow 12 x=24 $
$\Rightarrow=\frac{24}{12}=2$
So, the required point is $P (2,0)$
Then, $(PA)^2=(PB)^2$
$\Rightarrow(x+1)^2=(x-5)^2$
$\Rightarrow x^2+2 x+1=x^2-10 x+25$
$\Rightarrow 12 x=24 $
$\Rightarrow=\frac{24}{12}=2$
So, the required point is $P (2,0)$
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