Question

find the distance between the two points.

Explanation:

Step1: Identify the distance - formula

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

Step2: Assign the values of the points

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

Step3: Calculate the value inside the square - root

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

Answer:

$34$