First slide

Pair of straight lines

Question

The quadrilateral formed by the lines whose equations are given by $x^{2} - 5 x + 6 = 0$ and $y^{2} - 14 y + 40 = 0$ is

Moderate

A

Square
B

Rectangle
C

Rhombus
D

Parallelogram

Solution

$The given lines are x^{2} - 5 x + 6 = 0 and y^{2} - 14 y + 40 = 0$
$It implies that the equations of sides are quadrilateral are$
$x - 1 = 0, x - 5 = 0, y - 10 = 0, y - 4 = 0$
The sides of quadrilateral are vertical and horizontal lines, so angles are right angles
Distances between corresponding opposite sides are $5 - 1 = 4, 10 - 4 = 6$
Since the distances between two parallel sides are not equal, and the angles are right angles, the figure formed by the lines is rectangle.

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