Question

Distance of point (3, 4) from the origin is .................. .

• A. 7
• B. 1
• C. 5
• D. -5

Hint:

Recognize that the coordinates (3, 4) and the distance from the origin form a right-angled triangle with the axes. The distance is the hypotenuse. The sides are 3 and 4, which are part of the (3, 4, 5) Pythagorean triplet. This allows you to find the answer instantly without calculation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem requires finding the distance between a given point and the origin (0, 0) in a 2D Cartesian coordinate system.

Step 2: Key Formula or Approach:
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] When one point is the origin (0, 0) and the other is (x, y), the formula simplifies to:
\[ d = \sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{x^2 + y^2} \]

Step 3: Detailed Explanation:
We need to find the distance of the point (3, 4) from the origin (0, 0).
Here, \(x = 3\) and \(y = 4\).
Using the simplified distance formula:
\[ d = \sqrt{3^2 + 4^2} \] \[ d = \sqrt{9 + 16} \] \[ d = \sqrt{25} \] \[ d = 5 \] Distance is a scalar quantity and is always non-negative, so option (D) -5 is incorrect.

Step 4: Final Answer:
The distance of the point (3, 4) from the origin is 5 units.