Question

find the distance between the pair of points. (0,0) and (-8,6) the distance between the points is units.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-8,6)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,x_2=-8,y_2 = 6$ into the formula: $d=\sqrt{(-8 - 0)^2+(6 - 0)^2}=\sqrt{(-8)^2+6^2}$.

Step3: Calculate squares

$(-8)^2=64$ and $6^2 = 36$, so $d=\sqrt{64 + 36}$.

Step4: Add and find square - root

$64+36 = 100$, and $\sqrt{100}=10$.

Answer:

10