Given the points (0,0) and (8,4)
The midpoint will be the point M, which can be calculated as following :
[tex]M=\frac{(0,0)+(8,4)}{2}=\frac{(8,4)}{2}=(4,2)[/tex]The slope of the line segment with the endpoints (0,0) and (8,4) will be :
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{8-0}=\frac{4}{8}=\frac{1}{2}[/tex]So, the slope of the perpendicular to the given line segment = -2
So, the required line have a slope of -2 and passing through the point ( 4 , 2 )
The slope - point form of the line will be :
[tex](y-2)=-2(x-4)[/tex]And the general form will be :
[tex]\begin{gathered} y-2=-2x+8 \\ y=-2x+8+2 \\ \\ y=-2x+10 \end{gathered}[/tex]
