Question

If O(0, 0) be the origin and co-ordinates of the point P be (x, y) then the distance OP is

• A. \(\sqrt{x^2 - y^2}\)
• B. \(\sqrt{x^2 + y^2}\)
• C. \(x^2 - y^2\)
• D. none of these

Hint:

The distance of any point (x, y) from the origin (0, 0) is simply the square root of the sum of the squares of its coordinates. This is a direct consequence of the Pythagorean theorem.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question asks for the formula for the distance of a point from the origin in a Cartesian coordinate system. This is a direct application of the distance formula.

Step 2: Key Formula or Approach:
The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] We will apply this formula for the origin O(0, 0) and the point P(x, y).

Step 3: Detailed Explanation:
Let the two points be:
Point 1 (Origin O): \((x_1, y_1) = (0, 0)\).
Point 2 (Point P): \((x_2, y_2) = (x, y)\).
Substitute these coordinates into the distance formula:
\[ \text{Distance OP} = \sqrt{(x - 0)^2 + (y - 0)^2} \] \[ \text{Distance OP} = \sqrt{(x)^2 + (y)^2} \] \[ \text{Distance OP} = \sqrt{x^2 + y^2} \] This is the standard formula for the distance of a point from the origin.

Step 4: Final Answer:
The distance OP is \(\sqrt{x^2 + y^2}\).