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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.
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Solution
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:
\[y - 6 = \frac{4 - 6}{10 + 2}\left( x + 2 \right)\]
⇒ x + 6y − 34 = 0
And, the equation of BD passing through B (1, 2) and D (7, 8) is:
\[y - 2 = \frac{8 - 2}{7 - 1}\left( x - 1 \right)\]
⇒ x − y + 1 = 0
Hence, the equations of the diagonals are x + 6y − 34 = 0 and x − y + 1 = 0.
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