Question

The following set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral (four-sided figure)

Answer 1

To find the slope between those vertices, we can write the lines that contains each pair in slope-intercept form. The line equation in slope-intercept form is:

$y=mx+b$

Where m represents the slope and b the y-intercept.

To find those values we just need to substitute our pair of points on this form and create a system for m and b.

For our first pair of points (0, 1) and (-2, 5), we have

$\begin{gathered} b=1 \\ 5=-2m+b \\ \Rightarrow\begin{cases}b=1 \\ m=-2\end{cases} \end{gathered}$

The slope for the first pair is -2.

For the second pair (6, 2) and (4, 6) we have

$\begin{cases}2=6m+b \\ 6=4m+b\end{cases}$

Subtracting the first equation from the first, we get

$\begin{gathered} 2-(6)=6m+b-(4m+b) \\ -4=2m \\ m=-2 \end{gathered}$

The slope for the other side is also -2.