Question

what is the distance between (-7, -5) and (-1, 5)?
none of these
$2\sqrt{34}$
$4\sqrt{17}$
$6\sqrt{17}$
from drawing these points on a graph,
g pages at the end of this lesson’s
e sure to simplify the radical to get

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

Step3: Substitute into the formula

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

Step4: Simplify the radical

Factor 136: \( 136 = 4\times34 \), so \( \sqrt{136}=\sqrt{4\times34}=\sqrt{4}\times\sqrt{34}=2\sqrt{34} \).

Answer:

$2\sqrt{34}$ (corresponding to the option "2√34")