Question

Show that the distance between a point p(x,y) and the origin is √x^2 + y^2

Answer 1

The distance of the point P(X,Y) from the origin O(0,0) is given by ,

OP = under root (X-0)² + (Y-0)².

i.e,

OP = under root X² + Y².

y-x=(x+y)²

x²+y²-x+y=0

Explanation:

Answer 2

See below.

Explanation:

To find the distance between any two points, we can use the distance formula:

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`

We want to prove that the distance between a point P(x,y) and the origin is:

`d=√(x^2+y^2)`

Remember that the origin is at (0,0).

So, let's prove it using the distance formula. Let's let the origin point (0,0) be (x₁, y₁) and let's let P(x, y) be (x₂, y₂). Substitute these values into the distance formula. This yields:

`d=\sqrt{(x-0)^2+(y-0)^2`

Subtract:

`d=\sqrt{(x)^2+(y)^2`

Simplify:

`d=√(x^2+y^2)`

This is the same equation as given.

Q.E.D.