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}`