Question

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

Explanation:

Step1: Recall the 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, $x_1 = 6,y_1=4,x_2=-9,y_2 = - 4$.

Step2: Substitute the values into the formula

$d=\sqrt{(-9 - 6)^2+(-4 - 4)^2}=\sqrt{(-15)^2+(-8)^2}$.

Step3: Calculate the squares

$(-15)^2=225$ and $(-8)^2 = 64$, so $d=\sqrt{225 + 64}$.

Step4: Add the values inside the square - root

$225+64 = 289$, so $d=\sqrt{289}$.

Step5: Find the square - root

$\sqrt{289}=17$.

Answer:

17