Question

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

Explanation:

Step1: Identify the coordinates

From the graph, one point is \((0,1)\) (let it be \((x_1,y_1)\)) and the other is \((2,4)\) (let it be \((x_2,y_2)\)).

Step2: Substitute into the distance formula

Substitute \(x_1 = 0,y_1=1,x_2 = 2,y_2 = 4\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
We get \(d=\sqrt{(2 - 0)^2+(4 - 1)^2}=\sqrt{2^2+3^2}\).

Step3: Calculate the value

\(2^2=4\), \(3^2 = 9\), then \(2^2+3^2=4 + 9=13\). So \(d=\sqrt{13}\), and \(n = 13\).

Answer:

\(13\)