Question

The distance of the point m(-3, 4) from the origin is

• A. 5
• B. 6
• C. \( \sqrt{49} \)
• D. 1

Hint:

The coordinates (-3, 4) form a right-angled triangle with the origin, where the legs are the absolute values of the coordinates (3 and 4). This is a classic (3, 4, 5) Pythagorean triplet. Recognizing this allows you to find the distance (the hypotenuse) instantly without calculation.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question asks for the distance between a given point and the origin (0, 0) in a 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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] A special case is the distance from the origin (0,0) to a point (x, y), which simplifies to \( d = \sqrt{x^2 + y^2} \).
Step 3: Detailed Explanation:
The two points are the origin \( (0, 0) \) and point m \( (-3, 4) \).
Let \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (-3, 4) \).
Using the distance formula:
\[ d = \sqrt{(-3 - 0)^2 + (4 - 0)^2} \] \[ d = \sqrt{(-3)^2 + (4)^2} \] \[ d = \sqrt{9 + 16} \] \[ d = \sqrt{25} \] \[ d = 5 \] Step 4: Final Answer:
The distance of the point m(-3, 4) from the origin is 5 units. Note that option (C) \( \sqrt{49} \) is equal to 7.