Question

use the graph to determine the length of segment gm. enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point g: (?,?) coordinates (x2, y2) of point m: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2} d = \sqrt{( )^2+( 6 )^2} d = the length of segment gm is centimeters

Explanation:

Step1: Identify coordinates

From the graph, point G has coordinates $(-2,-7)$ and point M has coordinates $(-5, - 1)$. So $(x_1,y_1)=(-2,-7)$ and $(x_2,y_2)=(-5,-1)$.

Step2: Substitute into distance formula

The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1=-2,y_1 = - 7,x_2=-5,y_2=-1$ into it:
$d=\sqrt{(-5-(-2))^2+(-1 - (-7))^2}=\sqrt{(-5 + 2)^2+(-1 + 7)^2}=\sqrt{(-3)^2+6^2}$.

Step3: Calculate squares and sum

First, calculate $(-3)^2=9$ and $6^2 = 36$. Then $(-3)^2+6^2=9 + 36=45$. So $d=\sqrt{45}$.

Step4: Simplify square - root

$\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx 6.71$ (rounded to two decimal places).

Answer:

$3\sqrt{5}\approx6.71$