Question

given the coordinates (0, 0) and (4, 1), the distance is:
○ 16.
○ √17.
○ 17.
○ 1.

Explanation:

Step1: Recall Distance Formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify Coordinates

Here, \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (4, 1)\).

Step3: Substitute into Formula

Substitute values: \( d = \sqrt{(4 - 0)^2 + (1 - 0)^2} \).

Step4: Simplify Expression

Calculate squares: \( (4)^2 = 16 \), \( (1)^2 = 1 \). Sum: \( 16 + 1 = 17 \). So \( d = \sqrt{17} \).

Answer:

\(\sqrt{17}\) (corresponding to the option with \(\sqrt{17}\))