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Equation of line in Straight lines

Question

The area ( in square units) enclosed by 2|x|+3|y|6 is

Moderate
Solution

We have 2|x|+3|y|6 This is equivalent to the following system of inequations:

and, 2x+3y6, when x0,y02x3y6, when x0,y02x+3y6, when x0,y02x3y6, when x0,y0

These inequations form a rhombus having its diagonals of lengths 6 and 4 units, along the coordinate axes

So, required area =12(6×4)=12 sq. units



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The line x/3+y/3=1 meets the y-and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB way from the origin. The coordinates of the vertex of the square farthest from the origin are 


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