11. Find the distance between $P$ and $Q$ if $P$lies on the $y$ – axis and has an ordinate $5$ while $Q$ lies on the $x$ – axis and has an abscissa $12$.

Home » 11. Find the distance between and if lies on the – axis and has an ordinate while lies on the – axis and has an abscissa .

11. Find the distance between $P$ and $Q$ if $P$ lies on the $y$ – axis and has an ordinate $5$ while $Q$ lies on the $x$ – axis and has an abscissa $12$ .

Class 10 | Distance and Section Formulae | Frank | ICSE | Maths

11. Find the distance between $P$ and $Q$ if $P$ lies on the $y$ – axis and has an ordinate $5$ while $Q$ lies on the $x$ – axis and has an abscissa $12$ .

Distance – The length along a line or line segment between two points on the line or line segment.

Section formula define – The section formula helps in finding the coordinates of a point dividing the coordinates of a point dividing a given line segment into two parts such that their lengths are in a given ratio.

From the question it is given that,

P lies on the $y$ – axis and has an ordinate $5$ .

Then, point $P\left( 0,5 \right)$

And also in the question it is given that, $Q$ lies on the $x$ – axis and has an abscissa

$12$ .

So, point $Q\left( 12,0 \right)$

We know that, $PQ=\sqrt{\left( {{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}} \right)}$
Where, ${{x}_{1}}=x$ coordinate of $P=0$
${{y}_{1}}=y$ coordinate of $Q=5$
${{x}_{2}}=x$ coordinate of $P=12$
${{y}_{2}}=y$ coordinates of $Q=0$
$=\sqrt{\left( {{\left( 12-0 \right)}^{2}}+{{\left( 0-5 \right)}^{2}} \right)}$
$=\sqrt{\left( \left( 144 \right)+\left( 25 \right) \right)}$
$=\sqrt{\left( 169 \right)}$
$=13units$