Question

what is the distance between (-3, 4) and (2, -3)?
none of these
4√17
2√37
√74

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, \( x_1 = -3 \), \( y_1 = 4 \), \( x_2 = 2 \), \( y_2 = -3 \).

Step3: Substitute into Formula

Calculate \( x_2 - x_1 = 2 - (-3) = 5 \), \( y_2 - y_1 = -3 - 4 = -7 \).
Then \( d = \sqrt{(5)^2 + (-7)^2} = \sqrt{25 + 49} = \sqrt{74} \).

Answer:

\(\sqrt{74}\) (corresponding to the option with \(\sqrt{74}\))