Question

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

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

Step3: Substitute into formula

\( d = \sqrt{(0 - 2)^2 + (5 - (-3))^2} = \sqrt{(-2)^2 + (8)^2} \)

Step4: Simplify

\( \sqrt{4 + 64} = \sqrt{68} = \sqrt{4\times17} = 2\sqrt{17} \)

Answer:

\( 2\sqrt{17} \) (the option with \( 2\sqrt{17} \))