First slide

Equation of line in Straight lines

Question

The equations to a pair of opposite sides of a parallelogram are $x^{2} - 5 x + 6 = 0$ and $y^{2} - 6 y + 5 = 0$ . The equations to its diagonals, are

Moderate

A

$x + 4 y = 13$ and $y = 4 x - 7$
B

$4 x + y = 13$ and $4 y = x - 7$
C

$4 x + y = 13$ and $y = 4 x - 7$
D

$y - 4 x = 13$ and $y + 4 x = 7$

Solution

Solving the equations of the sides taken in pairs, we obtain
that the coordinates of the vertices $A, B, C, D$ of the
parallelogram $A B C D$ are $A (2, 1), B (3, 1), C (3, 5), D (2, 5)$
respectively. Hence, the equations of diagonals $A C$ and $B D$ are
$4 x - y - 7 = 0$ and $4 x + y - 13 = 0 .$

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