Question

what is the distance between (2, -3) and (0, 5)?
○ 4√7
○ 2√17
○ none of these
○ 4√15

Explanation:

Step1: Recall the distance formula

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

Step2: Identify the coordinates

Here, \((x_1, y_1) = (2, -3)\) and \((x_2, y_2) = (0, 5)\).

Step3: Substitute into the formula

Calculate the differences: \( x_2 - x_1 = 0 - 2 = -2 \) and \( y_2 - y_1 = 5 - (-3) = 8 \).
Then, \( d = \sqrt{(-2)^2 + 8^2} = \sqrt{4 + 64} = \sqrt{68} \).

Step4: Simplify the square root

Simplify \( \sqrt{68} \): \( \sqrt{4 \times 17} = \sqrt{4} \times \sqrt{17} = 2\sqrt{17} \).

Answer:

$2\sqrt{17}$ (corresponding to the option "2√17")