Question

The distance of a point, P on x-axis from A(11, 12) is 13 units. Find the coordinates of P.

Answer 1

Given that,

$P$ is a point on $x-axis$

The distance between $P$ and another point $A(11,12)$ is $13$ units.

To find out,

The coordinates of the point $P$.

Let the coordinates of point $P$ be $(h,0)$.

We know that, the distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore$ Distance between $A$ and $P$ $=\sqrt{(h-11{)}^2+(0-12{)}^2}=13$

$\Rightarrow \sqrt{(h-11{)}^2+144}=13$

Squaring both sides, we get:

$(h-11{)}^2+144={13}^2$

$\Rightarrow (h-11{)}^2=169-144$

$\Rightarrow (h-11{)}^2=25$

$\Rightarrow h-11=\pm 5$

$\Rightarrow h=16or6$

Hence, the coordinates of $P$ are either $(16,0)$ or $(6,0)$.