Question

what is the distance between (5, 3) and (-4, -3)?
9√13
13√9
3√13
none of these

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, \((x_1, y_1) = (5, 3)\) and \((x_2, y_2) = (-4, -3)\).

Step3: Substitute into the formula

Calculate \( x_2 - x_1 = -4 - 5 = -9 \) and \( y_2 - y_1 = -3 - 3 = -6 \). Then, \( d = \sqrt{(-9)^2 + (-6)^2} \).

Step4: Simplify the expression

\( (-9)^2 = 81 \) and \( (-6)^2 = 36 \), so \( d = \sqrt{81 + 36} = \sqrt{117} \). Simplify \( \sqrt{117} \): \( 117 = 9\times13 \), so \( \sqrt{117} = \sqrt{9\times13} = 3\sqrt{13} \).

Answer:

$3\sqrt{13}$ (corresponding to the option "3√13")