Question

finding the distance between two points in the coordinate plane
the distance between the two points pictured is ( d = sqrt{n} )
use the distance formula to find ( n ).
( d = sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} )
( n = )

Explanation:

Step1: Identify the coordinates of the two points

From the graph, the two points are \((-2,-2)\) and \((2,4)\). Let \((x_1,y_1)=(-2,-2)\) and \((x_2,y_2)=(2,4)\).

Step2: Substitute into the distance formula

Substitute \(x_1=-2,y_1 = - 2,x_2=2,y_2 = 4\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2-x_1=2-(-2)=2 + 2=4\)
\(y_2-y_1=4-(-2)=4 + 2=6\)
Then, calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\):
\((x_2 - x_1)^2+(y_2 - y_1)^2=4^2+6^2\)
\(=16 + 36\)
\(=52\)

Answer:

\(52\)