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
$AP^2=BP^2$
$\Rightarrow(7-x)^2+(6-0)^2=(-3-x)^2+(4-0)^2$
$\Rightarrow 49-14 x+x^2+36=9+6 x+x^2+16$
$\Rightarrow 85-14 x=6 x+25$
$\Rightarrow 20 x=60$
$\Rightarrow x=3$
Thus, the point $(3,0)$.
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