Question

pablo and nadia are playing a game on a coordinate grid. pablo puts a playing piece point (-2,3) and nadia puts a playing piece at (3, -1). what is the distance between the two playing pieces?

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 $(x_2,y_2)=(3,-1)$.

Step2: Calculate differences

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

Step3: Square differences and sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=5^2+(-4)^2=25 + 16=41$.

Step4: Take square - root

$d=\sqrt{41}$.

Answer:

$\sqrt{41}$