Question

Find, in radical form, the distance between (2, 1) and (-1,3).

Answer 1

You have the following two points:

(2,1)

(-1,3)

In order to determine what is the distance between the previous points, you use the following formula:

$d=\sqrt[]{(x_1-x_2)^2-(y_1-y_2_{}^{})^2}$

where (x1,y1) and (x2,y2) are the points with a distance between them of d.

You use the given points to replace them into the formula for d:

$\begin{gathered} d=\sqrt[]{(1-3)^2-(2-(-1))^2} \\ d=\sqrt[]{(-2)^2+(3)^2} \\ d=\sqrt[]{4+9} \\ d=\sqrt[]{13} \end{gathered}$

hence, the distance between the given points is √13