Roads Layout and Intersection: Four road R1, R2,R3,R4 are laid in such a way that R1, R2 are mutually perpendicular whereas R3 and R4 intesect. Taking R1 as x-axis R2 are y-axis. Equation of R3 and R1 are given by equations 4x + 2y - 4 = 0 and 2x + y - 6 = 0. Equation of R1 is a) x = 0 b) y = 0 c) x + y = 2 d) x - y = 2 ii) Equation of R2 is a) x + 2 = 0 b) x = 0 c) y = 0 d) y - 2 = 0 iii) Which of the following is true ? a) R3 and R4 are parallel roads. b) R3 and R4 are actually one and same road.
Answers
Given : Four road R1, R2,R3,R4 are laid in such a way that R1, R2 are mutually perpendicular whereas R3 and R4 intersect.
R1 is x-axis R2 is y-axis.
Equation of R3 4x + 2y - 4 = 0 and
Equation of R4 2x + y - 6 = 0.
To Find :
Equation of R1
Equation of R2
Which of the following is true
a) R3 and R4 are parallel roads. b) R3 and R4 are actually one and same road.
Solution:
R1 is x-axis , y = 0 is the equation for x -axis
correct option is b) y = 0
R2 is y-axis , x = 0 is the equation for y -axis
correct option is b) x= 0
Equation of R3 4x + 2y - 4 = 0 and
Equation of R4 2x + y - 6 = 0.
4/2 = 2/1 ≠ -4/(-6)
2 = 2 ≠ 2/3
Hence lines are parallel
so R3 and R4 are parallel roads.
Correct option is a) R3 and R4 are parallel roads
Pair of linear equations
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Consistent
if a₁/a₂ ≠ b₁/b₂ (unique solution and lines intersects each others)
a₁/a₂ = b₁/b₂ = c₁/c₂ (infinite solutions and line coincide each other )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution , lines are parallel to each other)
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