Coordinate Geometry - Study Mode

[#81] If a linear equation is of the form x = k where k is a constant, then graph of the equation will be
Correct Answer

(D) a line parallel to y-axis

Explanation

Solution: x = k, where k is a constant The graph of the equation will be parallel to y-axis.

[#82] The total area (in sq. unit) of the triangles formed by the graph of 4x + 5y = 40, x-axis, y-axis and x = 5 and y = 4 is:
Correct Answer

(B) 20

Explanation

Solution: $$eqalign{
& 4x + 5y = 40 cr
& Rightarrow frac{x}{{10}} + frac{y}{8} = 1 cr} $$ Intersection point of 4x + 5y = 40 and y = 4 will be, 4x + 5 × 4 = 40 4x = 20 x = 5 ∴ Intersecting point is (5, 4) Area of ΔABC = $$frac{1}{2}$$ × (10 - 5) × 4 = 10 sq. units Area of ΔCDE = $$frac{1}{2}$$ × 5 × (8 - 4) = 10 sq. units ∴ Area bounded by the graph = 10 + 10 = 20 sq units.

[#83] The linear equation such that each point on its graph has an ordinate four times its abscissa is:
Correct Answer

(B) y = 4x

Explanation

Solution: Since ordinate is four times its abscissa, equation of line will be y = 4x

[#84] What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?
Correct Answer

(C) 3

Explanation

Solution: $$eqalign{
& ,,x + y = 3 cr
& underline {,2x + 5y = 12,} cr
& ,,,,,,,,,,y = 2 cr} $$ Area of ΔABC = $$frac{1}{2}$$ × 3 × 2 = 3

[#85] Equation of the straight line parallel to x-axis and also 3 units below x-axis is:
Correct Answer

(C) y = -3

Explanation

Solution: Equation of straight line parallel to x-axis and also 3 units below x-axis is y = -3