The vertices of a quadrilateral are A (-2, 6), B (1, 2), C (10, 4… - Vidyadip

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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Answer

The quadrilateral ABCD has diagonals AC and BD.The required equation is
Since, A(-2, 6), C(10, 4), the equation for AC is:
$\text{y}-6=\frac{4-6}{10-(-2)}(\text{x}-(-2))\ \Big[\text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)\Big]$
$\text{y}-6=-\frac{12}{6}(\text{x}+2)$
$\text{y}-6=\frac{-(\text{x}+2)}{6}$
$\text{6y}-36=-\text{x}-2$
$\text{x}+\text{6y}-34=0$
Since, B(1, 2), D(7, 8), the equation for BD is:
$\text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)$
$\text{y}-2=\frac{8-2}{7-1}(\text{x}-1)$
$\text{y}-2=\frac{6}{6}(\text{x}-1)$
$\text{y}-2=\text{x}-1$
$\text{x}-\text{y}+1=0$

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