Question

find the length of the segment connecting (6, 9) and (7, 4). provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(6,9)$ and $(x_2,y_2)=(7,4)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=7 - 6 = 1$ and $y_2 - y_1=4 - 9=-5$.

Step3: Square the differences

$(x_2 - x_1)^2=1^2 = 1$ and $(y_2 - y_1)^2=(-5)^2 = 25$.

Step4: Sum and square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{1 + 25}=\sqrt{26}\approx5.1$.

Answer:

$5.1$