Solution:
To find the slope, m, of a straight line, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For line AC,
Picking coordinates from the graph
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,5) \\ (x_2,y_2)\Rightarrow(4,4) \end{gathered}[/tex]
Substitute the coordinates into the formula to find the slope, m, of a straight line
[tex]m=\frac{4-5}{4-2}=\frac{-1}{2}=-\frac{1}{2}[/tex]
For line DC
Picking coordinates from the graph
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(4,4) \\ (x_2,y_2)\Rightarrow(6,8) \end{gathered}[/tex]
Substitute the coordinates into the formula to find the slope, m₁, of a straight line
[tex]m=\frac{8-4}{6-4}=\frac{4}{2}=2[/tex]
Line AC and DC are perpendicular, i.e.
[tex]m\times m_1=-\frac{1}{2}\times2=-1[/tex]
Hence,
[tex]mm_1=-1[/tex]
