Question

Ramu says the distance of a point P(x1, y1) from the origin O(0, 0) is √x² + y² . Do you agree with Ramu or not? Why?

Answer 1

Yes,

let the point be (x,y) and origin is (0,0)

distance=√[(x2-x1)²+(y2-y1)²]

from given points we get distence=√[(x-0)²+(y-0)²]

hence distance = √(x²+y²)

Answer 2

it is given that, Ramu said “ the distance of a point P(x₁, y₁) from the origin O (0, 0) is $\sqrt{x_1^2+y_1^2}$.

let me check it is correct or not...

we know, distance between two points (x₁, y₁) and (x₂, y₂) is given as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

so distance of a point P((x₁, y₁) from origin O is OP

= $\sqrt{(x_1-0)^2+(y_1-0)^2}$

= $\sqrt{x_1^2+y_1^2}$

here we also get the same result.

therefore we agree with Ramu and reason behind it is explained in above explanation as you can see.