Question

find the distance between the two points. (1,-3) (4,2)

Explanation:

Step1: Identify the 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, $(x_1,y_1)=(1, - 3)$ and $(x_2,y_2)=(4,2)$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4 - 1=3$ and $y_2 - y_1=2-( - 3)=2 + 3 = 5$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=5^2 = 25$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 25=34$.

Step4: Take the square - root

$d=\sqrt{34}$.

Answer:

$\sqrt{34}$