Question

The vertices of a quadrilateral are A (−2, 6), B (1, 2), C (10, 4) and D (7, 8). Find the equation of its diagonals.

Answer 1

The two diagonals of the quadrilateral with vertices A (−2, 6), B (1, 2), C (10, 4) and D (7, 8) are AC and BD.

The equation of AC passing through A (−2, 6) and C (10, 4) is

$$\begin{gathered} y-6=\frac{4-6}{10+2}\left(x+2\right) \\ \Rightarrow x+6y-34=0 \end{gathered}$$

And, the equation of BD passing through B (1, 2) and D (7, 8) is

$$\begin{gathered} y-2=\frac{8-2}{7-1}\left(x-1\right) \\ \Rightarrow x-y+1=0 \end{gathered}$$

Hence, the equations of the diagonals are $x+6y-34=0$ and $x-y+1=0$