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Prove that the diagonals of the parallel...

Prove that the diagonals of the parallelogram formed by the four straight lines : `sqrt3x+y=0, sqrt3y+x=0`, `sqrt3x+y=1 and sqrt3y+x+1` are at right angle to one another.

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MODERN PUBLICATION-STRAIGHT LINES -EXERCISE
  1. What are inclinations to the x-axis of the st. lines : y=1/3x sqrt3+3 ...

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  2. Prove that the points (2, - 1), (0, 2), (3, 3) and (5,0) are the verti...

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  3. Prove that the diagonals of the parallelogram formed by the four strai...

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  4. The equations of three lines are given by : 15x -8y +1 =0, 12x+5y-3=0 ...

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  5. The three sides AB, BC, CA of a triangle are 5x - 3y +2 = 0,x-3y-2=0 a...

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  6. Find the equation of the line through the point (0, 2) making an angle...

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  7. Find the point of intersection of the straight lines : 2x + 3y-6 = 0...

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  8. Find the point of intersection of the straight lines : x= 0, 2x-y +3...

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  9. Find the point of intersection of the straight lines : x/3-y/4=0, x/...

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  10. Two lines cut the axis of x at distances of 4 and -4 and the axis of y...

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  11. If ax-2y-1=0 and 6x-4y+b=0 represent the same line, find the values of...

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  12. The line 2x-3y=4 is perpendicular bisector of the line AB. If the coor...

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  13. Show that the straight lines : x-y-1=0, 4x + 3y = 25 and 2x-3y + 1 = 0...

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  14. For what value of K are the three st. lines : 2x+y-3=0, 5x + ky-3=0 ...

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  15. For what value of K are the three st. lines : 3x+y-2=0,kx+ 2y-3=0 an...

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  16. If the lines whose equations are y=m1x+c1,y=m2x+c2and y=m3x+c3 are con...

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  17. Find the condition that the st. lines : p1x+q1y=1,p2x+q2y=1 and p3x+q3...

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  18. Find the foot of the perpendicular from the point (-1, 2) on the st. l...

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  19. Prove that the diagonals of the parallelogram formed by the four lines...

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  20. Prove that the following lines are concurrent. Also, find the point of...

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