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Question

For the quadrilateral formed by the lines 4y3x1=0, 3y+4x+1=0, 4y3x2=0 and 3y+4x+2=0, which among the following statements are true

A
Quadrilateral formed will be square.
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B
Area of quadrilateral formed is 125 Sq. units.
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C
Slope of diagonals of quadrilateral are 7,17
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D
Slope of diagonals of quadrilateral are 3,13
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Solution

The correct option is C Slope of diagonals of quadrilateral are 7,17
L1:3x+4y1=0, m1=34
L2:4x+3y+1=0, m2=43
L3:3x+4y2=0, m3=34
L4:4x+3y+2=0, m1=43

Opposite sides are parallel and adjacent sides are perpendicular. So given quadrilateral can be square or rectangle.
distance between L1 and L3= distance between L2 and L4=15 units
Given quadrilateral represents square, where side length=15


Area of square=125 Sq. units
Let slope of diagonal AC be m as it is equally inclined to lines AB andAD
(43)m1+(43)(m)=⎜ ⎜ ⎜ ⎜(34)m1+(34)(m)⎟ ⎟ ⎟ ⎟
4+3m34m=34m4+3m
(3m+4)2=(34m)2
3m+4=±(34m)
3m+4=34m (or) 3m+4=3+4m
m=1/7 or m=7

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