Question

find the distance between the points a (13, 2) and b (7, 10). the distance between the two points is

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, $x_1 = 13,y_1 = 2,x_2 = 7,y_2 = 10$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=7 - 13=-6$ and $y_2 - y_1 = 10 - 2 = 8$.

Step3: Square the differences

Square the results from step 2. $(-6)^2=36$ and $8^2 = 64$.

Step4: Sum the squared - differences

Add the squared results: $36+64 = 100$.

Step5: Take the square - root

$d=\sqrt{100}=10$.

Answer:

10