Question

This is my assignment and we had to do our own, the teachers one made sense, but I just want to know if I am correct on the equations. It's Distance Formula. :)

Answer 1

The distance between two points can be calculated using the formula;

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

Given the two points;

$\begin{gathered} A(3,2) \\ B(3,5) \end{gathered}$

Substituting the coordinates, we have;

$\begin{gathered} AB=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ AB=\sqrt[]{(5-2_{})^2+(3_{}-3_{})^2} \\ AB=\sqrt[]{(3)^2+(0_{})^2} \\ AB=\sqrt[]{9} \\ AB=3 \end{gathered}$

For the second point;

$\begin{gathered} A^{\prime}(3,-2) \\ B^{\prime}(3,-5) \end{gathered}$

Substituting the coordinateswe have;

$\begin{gathered} A^{\prime}B^{\prime}=\sqrt[]{(-5-(-2)_{})^2+(3_{}-3_{})^2} \\ A^{\prime}B^{\prime}=\sqrt[]{(-5+2_{})^2+(0_{})^2} \\ A^{\prime}B^{\prime}=\sqrt[]{(-3)^2+0} \\ A^{\prime}B^{\prime}=\sqrt[]{9} \\ A^{\prime}B^{\prime}=3 \end{gathered}$

Therefore;

$\begin{gathered} AB=3 \\ A^{\prime}B^{\prime}=3 \end{gathered}$