pablo and nadia are playing a game on a coordinate grid. pablo puts a playing piece at point (-2,3) and…

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

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

Answer

Answer:

$\sqrt{41}$

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

Step3: Calculate squares

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

Step4: Sum squares and find square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{25 + 16}=\sqrt{41}$.