Question

learning target: find the distance of two poi

1. find the distance ab of a(3, 5) and b(9, 25)

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 $x_1 = 3,y_1 = 5,x_2=9,y_2 = 25$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=9 - 3=6$ and $y_2 - y_1=25 - 5 = 20$.

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=20^2=400$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 400=436$.

Step5: Calculate the square - root

$d=\sqrt{436}=\sqrt{4\times109}=2\sqrt{109}$.

Answer:

$2\sqrt{109}$