Question

The distance of a point P(x, y) from the
origin
​

Answer 1

Step-by-step explanation:

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=

OQ

2

+QP

2

=

x

2

+y

2

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

x

2

+y

2