Given the coordinates;
[tex]\begin{gathered} M(4,-4) \\ N(2,0) \end{gathered}[/tex]
The slope m of the line MN is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where x}_1=4,y_1=-4,x_2=2,y_2=0 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{0-(-4)}{2-4} \\ m=\frac{4}{-2} \\ m=-2 \end{gathered}[/tex]
The slope of a line parallel to the line MN must have a slope equal to line MN, that is;
[tex]\mleft\Vert m=-2\mright?[/tex]
The slope of a line perpendicular to line MN has a slope of negative reciprocal of line MN, that is;
[tex]\begin{gathered} \perp m=-\frac{1}{-2} \\ \perp m=\frac{1}{2} \end{gathered}[/tex]
Using the distance formula to find the length of MN, the formula is given as;
[tex]D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} \text{Where x}_1=4,y_1=-4,x_2=2,y_2=0 \\ |MN|=\sqrt[]{(0-(-4)^2+(2-4)^2} \\ |MN|=\sqrt[]{16+4} \\ |MN|=\sqrt[]{20} \\ |MN|=4.5 \end{gathered}[/tex]
