Question

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

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, $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(2,4)$.

Step2: Calculate differences

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

Step3: Square the differences

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=1^2 = 1$.

Step4: Sum and take square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{16 + 1}=\sqrt{17}$.

Answer:

$\sqrt{17}$