Explanation
Step 1
if ABCD is a square then, the segment AB must be perpendicular to segment BC
it means,( if two lines are perpendicular, the product of the slopes is -1)
[tex]\text{slope}1\cdot\text{slope}2=-1\text{ equation (1)}[/tex]Step 2
find the slope of segment AB
Let P1(2,1) P2(4,4)
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{replacing} \\ \text{slope}=\frac{4-1}{4-2} \\ \text{slope1}=\frac{3}{2} \end{gathered}[/tex]Step 3
replace in equation (1) to find the slope of side BC
[tex]\begin{gathered} \frac{3}{2}\cdot\text{slope}2=-1 \\ \text{slope}_{2=}-1\cdot\frac{2}{3} \\ \text{slope}2=-\frac{2}{3} \end{gathered}[/tex]slope2= slope of side BC
I hope this helps you
