Question

calculate the distance between the points e=(-2, -3) and m=(1, 1) in the coordinate plane. give an exact answer (not a decimal approximation).

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

Step3: Calculate distance

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

$5$