Question

find the distance of a point P(x,y) from the origin.

Answer 1

Let O and P denote the points

( 0,0 ) and P( x,y ) and ' O ' be the

Origin .

The ∆OAP is a right angle

triangle .

From the figure ,

OA = x units

AP = y units

Hence , by using Pythagorean

Theorem ,

OP² = OA² + AP²

= x² + y²

OP = √x² + y²

Therefore ,

Distance of the point P(x,y)

From the origin = OP

= √x² + y²

••••

Answer 2

Given:

Point ( x, y )

Origin ( 0, 0 )

To find:

The distance.

Solution:

By formula

Distance between two points = √(( y2 - y1 )^2 + ( x2 - x1 )^2)

Origin ( 0, 0 ) ( x1, y1 )

Point ( x, y ) ( x2, y2 )

Distance = √(( y - 0 )^2 + ( x - 0 )^2

√(x)^2 + (y)^2  

Hence, the distance of a point P(x,y) from the origin is √(x)^2 + (y)^2.

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