Question

The distance between points (3, 0) and (0, -3) is :

• A. 3 units
• B. 6 units
• C. \(\sqrt{6}\) units
• D. \(\sqrt{18}\) units

Hint:

When one coordinate of each point is zero, the distance is simply the hypotenuse of a right triangle with legs equal to the non-zero coordinate values. Here, \(\sqrt{3^2 + 3^2}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The distance between two points in a 2D plane is the length of the shortest line segment connecting them, calculated using the coordinates of the points.
Step 2: Key Formula or Approach:
Distance \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Step 3: Detailed Explanation:
1. Assign coordinates: \((x_1, y_1) = (3, 0)\) and \((x_2, y_2) = (0, -3)\).
2. Substitute into the formula:
\[ d = \sqrt{(0 - 3)^2 + (-3 - 0)^2} \] \[ d = \sqrt{(-3)^2 + (-3)^2} \] \[ d = \sqrt{9 + 9} = \sqrt{18} \] 3. Note: \(\sqrt{18}\) can also be written as \(3\sqrt{2}\) units.
Step 4: Final Answer:
The distance is \(\sqrt{18}\) units.