Question

The distance between the points (0, 0) and (5, 12) is

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

The Correct Option is C

To solve the problem, we need to find the distance between the points \((0, 0)\) and \((5, 12)\). The formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a Cartesian plane is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Step 1: Identify the coordinates.
The given points are \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (5, 12)\).

Step 2: Substitute the coordinates into the distance formula.
Substituting the values, we get:

\[ d = \sqrt{(5 - 0)^2 + (12 - 0)^2} \]

Step 3: Simplify the expression inside the square root.
This simplifies to:

\[ d = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} \]

Step 4: Calculate the square root.
We know that \(\sqrt{169} = 13\).

Final Answer:
The distance between the points \((0, 0)\) and \((5, 12)\) is \(13\).

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