Question

in exercises 21 - 28, find the distance between the two points. 25. a(-8,0) and k(1,4)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-8,y_1 = 0,x_2=1,y_2 = 4$.

Step2: Calculate differences

$x_2 - x_1=1-(-8)=9$ and $y_2 - y_1=4 - 0 = 4$.

Step3: Square the differences

$(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=4^2=16$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 16=97$.

Step5: Take square - root

$d=\sqrt{97}$.

Answer:

$\sqrt{97}$