Question

if the distance between p (x,y) from orgin is 10 units the coordinates of p is ​

Answer 1

Let O be the origin and Q be the foot of the perpendicular dropped from P onto the x axis.

So ΔOPQ is right-angled at Q.

By definition of coordinates:

OQ=x coordinate of P= distance of P from y axis =∣x∣

Similarly, QP=∣y∣.

Thus, by using Pythagoras theorem on ΔOPQ, we get OP=

$</p><p>OQ2+QP2=x2+y2$

Thus the distance of the point P(x,y) from the origin O(0,0) is

$x </p><p>2</p><p> +y </p><p>2</p><p>$

Answer 2

Let O be the origin and Q be the foot of the perpendicular dropped from P onto the x axis.

So ΔOPQ is right-angled at Q.

By definition of coordinates:

OQ=x coordinate of P= distance of P from y axis =∣x∣

Similarly, QP=∣y∣.

Thus, by using Pythagoras theorem on ΔOPQ, we get OP= √OQ²+QP²

=√X²+Y²

Thus the distance of the point P(x,y) from the origin O(0,0) is √X²+Y²