Question

How do I find the distance formula A(-7,10) + B(-11,4)

Answer 1

We can use the distance formula to find the distance between A and B.

Given,

$\begin{gathered} (x_1,y_1)=(-7,10) \\ (x_2,y_2)=(-11,4) \end{gathered}$

The distance formula is

$D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$

Substituting in the respective points and simplifying, we can find the distance:

$\begin{gathered} D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ D=\sqrt[]{(4-10_{})^2+(-11-(-7))^2} \\ D=\sqrt[]{(-6)^2+(-4)^2} \\ D=\sqrt[]{36+16} \\ D=\sqrt[]{52} \\ D=\sqrt[]{4\cdot13} \\ D=\sqrt[]{4}\sqrt[]{13} \\ D=2\sqrt[]{13} \end{gathered}$

**Note

The radical property used to simplify the last steps are:

$\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}$

Answer$2\sqrt[]{13}$