Question

Calculate the distance of point P (x, y) from origin O.​

Answer 1

Answer:

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