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.
$(2, 0)$
Since the point lies on the $x-$axis, let the point be $P$
and its coordinates be $(x, 0).$
Given that the point is equidistant from the points $A$ and $B$.
$\Rightarrow\text{PA}=\text{PB}$
$\Rightarrow\sqrt{\text{(x}+1)^2}=\sqrt{\text{(x}-5)^2}$
$\Rightarrow(\text{x}+1)^2=(\text{x}-5)^2$
$\Rightarrow\text{x}^2+2\text{x}+1=\text{x}^2-10\text{x}+25$
$\Rightarrow2\text{x}+1=-10\text{x}+25$
$\Rightarrow12\text{x}=24$
$\Rightarrow\text{x}=2$
Hence, the point is $(2,0)$.
and its coordinates be $(x, 0).$
Given that the point is equidistant from the points $A$ and $B$.
$\Rightarrow\text{PA}=\text{PB}$
$\Rightarrow\sqrt{\text{(x}+1)^2}=\sqrt{\text{(x}-5)^2}$
$\Rightarrow(\text{x}+1)^2=(\text{x}-5)^2$
$\Rightarrow\text{x}^2+2\text{x}+1=\text{x}^2-10\text{x}+25$
$\Rightarrow2\text{x}+1=-10\text{x}+25$
$\Rightarrow12\text{x}=24$
$\Rightarrow\text{x}=2$
Hence, the point is $(2,0)$.
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