MathematicsState whether the given statement is true or false.The distance of a points P(x,y) from the origin is x2-y2.

State whether the given statement is true or false.

The distance of a points P(x,y) from the origin is $\sqrt{x^{2} - y^{2}}$ .

We have been given,
The distance of a points P(x,y) from the origin is

\sqrt{x^{2} - y^{2}}

.
Using distance formula,

D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

The origin's coordinates are known to be (0,0).
So, the distance of the point (x,y) from the origin must be,
Substituting

x_{2} = x, x_{1} = 0, y_{2} = y, and y_{1} = 0

, in the formula,

(x − 0) 2 + (y − 0) 2 = x 2 + y 2

Therefore, our statement is false.
The distance of a points P(x,y) from the origin is

\sqrt{x^{2} + y^{2}}

.
Hence, option 2 is correct.

JEE