Question

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

Explanation:

Step1: Identify distance formula

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

Step2: Assign values

Let $(x_1,y_1)=(13,2)$ and $(x_2,y_2)=(7,10)$. Then $x_2 - x_1=7 - 13=-6$ and $y_2 - y_1=10 - 2 = 8$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=8^2=64$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Calculate distance

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

Answer:

10