Question

what is the distance between $(-7, -5)$ and $(-1, 5)$?
$\bigcirc\\ 4\sqrt{17}$
$\bigcirc\\ 2\sqrt{34}$
$\bigcirc\\ 6\sqrt{17}$
$\bigcirc\\ $none of these

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, \( x_1 = -7 \), \( y_1 = -5 \), \( x_2 = -1 \), \( y_2 = 5 \).

Step3: Substitute into formula

Calculate \( x_2 - x_1 = -1 - (-7) = 6 \), \( y_2 - y_1 = 5 - (-5) = 10 \).
Then \( d = \sqrt{(6)^2 + (10)^2} = \sqrt{36 + 100} = \sqrt{136} \).

Step4: Simplify the square root

\( \sqrt{136} = \sqrt{4 \times 34} = 2\sqrt{34} \).

Answer:

B. \( 2\sqrt{34} \)