Given: the two diagonals of the quadrilateral with vertex A (-2, 6), B(1, 2), C(10, 4) and D(7, 8) are

AC and BD.

Concept Used:

The equation of the line passing through the two points ( x₁, y₁) and ( x₂, y₂).

To find:

The equation of diagonal of the quadrilateral.

Explanation:

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

Formula used:

y – 6 (x + 2)

⇒ x + 6y – 34 = 0

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

Formula used:

y – 2 (x – 1)

⇒ x – y + 1 = 0

Hence, the equation of the diagonal are x + 6y – 34 = 0 and x – y + 1 = 0