Question

15 determine and state the length of a line segment whose endpoints are (6,4) and (-9,-4).

Explanation:

Step1: Recall distance formula

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

Step2: Identify the values of coordinates

Let $(x_1,y_1)=(6,4)$ and $(x_2,y_2)=(-9,-4)$. Then $x_2 - x_1=-9 - 6=-15$ and $y_2 - y_1=-4 - 4=-8$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-15)^2 = 225$ and $(y_2 - y_1)^2=(-8)^2 = 64$. The sum is $225+64 = 289$.

Step4: Find the square - root

$d=\sqrt{289}=17$.

Answer:

$17$