Question

The coordinates of two vertices of a square ABCD are A(2,1) and B(4,4). Determine the slope of BC.

Answer 1

let us first find the slope of AB so \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
A&({\color{red}{ 2}}\quad ,&{\color{blue}{ 1}})\quad B&({\color{red}{ 4}}\quad ,&{\color{blue}{ 4}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\)

what would that give us for the slope of AB?

Answer 2

keep in mind that, A and B and C and D are coordinates of a SQUARE so whether C is up or down from B
since it's a square, it will make a PERPENDICULAR LINE to the line AB

and thus it's slope will be the NEGATIVE RECIPROCAL of the slope of AB