CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
MCQ
Which point on $x-$axis is equidistant from the points $A(7, 6)$ and $B(-3, 4)?$
A
$(0, 4)$
B
$(-4, 0)$
✓
$(3, 0)$
D
$(0, 3)$
✓
Answer
Correct option: C.
$(3, 0)$
Let the coordinates of the point be $P(x, 0)$
Since the point lies on the $x-$axis.
$P$ is equidistant from $A(7, 6)$ and $B(-3, 4)$
Using the distance from, we get
$ A P^2=B P^2 $
$ \Rightarrow(7-x)^2+(6-0)^2=(-3-x)^2+(4-0)^2 $
$\Rightarrow 49-14 x+x^2+36=9+6 x+x^2+16 $
$\Rightarrow 85 - 14x = 6x + 25$
$\Rightarrow 20x = 60$
$\Rightarrow x = 3$
Thus, the point $(3, 0).$
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