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Prove that the diagonals of the parallelogram formed by the lines `sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1` are at right angles.

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MODERN PUBLICATION-STRAIGHT LINES -Exercise 10(f)
  1. Find the equation of the st.line going through the point (1,-2) and pe...

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  2. Find the equation of a line passing through (4,5) and perpendicular to...

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  3. Find the equation of a line perpendicular to 2x+4y-9=0 and passing thr...

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  4. Find the equation of the line perpendicular to the line x-7y+5=0 and h...

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  5. Find the equation of a line that is perpendicular to 3x+2y=8 and passe...

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  6. Find the equation of the right bisector of the line segment joining...

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  7. Find the equation of the line passing through (-3,5) and perpendicular...

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  8. The equation of the line, which is perpendicular to 5x-2y=7 and passes...

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  9. Find the equation of a st.line drawn at right angles to the st.line (x...

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  10. The perpendicular from the origin to a line meets it at the point (-2,...

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  11. The perpendicular from the origin to the line y=mx+c meets it at the p...

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  12. Two lines passing through the point (2, 3) intersects each other at a...

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  13. Show that the equation of the passing through the origin and making a...

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  14. If the lines y" "=" "3x" "+" "1 and 2y" "=" "x" "+" "3 are equally ...

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  15. If the coordinates of the points A,B,C be (-1,5),(0,0) and (2,2) respe...

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  16. What are inclinations to the x-axis of the st.lines : y=(1)/(3)xsqrt(3...

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

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  18. Prove that the diagonals of the parallelogram formed by the lines sqrt...

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

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  20. Three sides A B ,A Ca n dC A of triangle A B C are5x-3y+2=0,x-3y-2=0a ...

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