Question

Find the distance between the points $(3,0)$ and $(0,4)$ without using the distance formula.

Answer 1

From the diagram,

Distance from origin in the $x-$axis$=3$ units.

Distance from origin in the $y-$axis$=4$ units.

$\therefore OA=3units$

$OB=4units$

Join $AB$

$\Rightarrow △AOB$ is right angled triangle.

Applying Pythagoras theorem,${AB}^2={OA}^2+{OB}^2$

$\Rightarrow {AB}^2=3^2+4^2=9+16=25$

$\therefore$Distance between the points$=AB=\sqrt{25}=5units$