Question

The area enclosed by 2|x| + 3|y≤ 6 is

Solution

Correct option is

12 sq. units

The given inequality is equivalent to the following system of inequalities. (Fig)     

                      2x + 3y ≤ 6, when x ≥ 0, y ≥ 0

                      2x – 3y ≤ 6, when x ≥ 0, y ≤ 0

                    –2x + 3y ≤ 6, when x ≤ 0, y ≥ 0

                    –2x – 3y ≤ 6, when x ≤ 0, y ≤ 0  

Which represents a rhombus with sides

                      2x ± 3y = 6 and 2x ± 3y = –6    

Length of the diagonals is 6 and 4 units along x-axis and y-axis.

∴         The required area = 1/2 × 6 × 4 = 12 sq. units.                                                         

                                                   

 

SIMILAR QUESTIONS

Q1

 

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

Q2

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

Q3

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

Q4

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q5

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Q6

If abc are unequal and different from 1 such that the points  are collinear, then  

Q7

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q8

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

                                                          

Q9

If P is a point (xy) on the line, y = –3x such that P and the point (3, 4) are on the opposite sides of the line 3x – 4y = 8, then   

 

Q10

Let O be the origin, A (1, 0) and B (0, 1) and P (xy) are points such thatxy > 0 and x + y < 1, then