Question

The distance from the origin O of A(x, y) is OA = . t,y,ty)​

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=

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

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Answer 2

Step-by-step explanation:

Distance between two points (x

1

,y

1

) and (x

2

,y

2

) is

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Distance of (x,y) from origin is

(x−0)

2

+(y−0)

2

=

x

2

+y

2