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If the vertices of a trianglehave integr...

If the vertices of a trianglehave integral coordinates, prove that the trinagle cannot be equilateral.

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. One end of a thin straight elastic string is fixed at A(4,-1) and the ...

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  2. Find the centroid and incentre of the triangle whose vertices are (2, ...

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  3. If the vertices of a trianglehave integral coordinates, prove that the...

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  4. Show that the equation of the locus of a point which moves so that the...

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  5. A stick of length l slides with its ends on two mutually perpendicular...

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  6. if x and y coordinates of a point P in x-y plane are given by x=(ucosa...

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  7. A straight line L is perpendicular to the line 5x-y=1 . The area of th...

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  8. Find the equation of the line passing through the point (2,3) and maki...

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  9. The equation of the straight line through the point of intersection of...

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  10. Find the points on the line x+y=4 that lies at a unit distance from th...

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  11. A line is such that its segment between the lines 5x -y+4=0 and 3x +4y...

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  12. lines L1:ax+by+c=0 and L2:lx+my+n=0 intersect at the point P and make ...

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  13. The st. lines 3x + 4y =5 and 4x-3y = 15 interrect at a point A(3,-1)....

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  14. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

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  15. If (h, r) is the foot of the perpendicular from (x1, y1) to lx+my+n=0,...

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  16. Equations of two straight lines are xcos alpha + ysin alpha = p and xc...

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  17. The side AB,BC,CD and DA of a quadrilateral are x+2y=3, x=1, x-3y=4, 5...

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  18. Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E...

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  19. Show that the lines 4x+y-9=0,x-2y+3=0,5x-y-6=0 make equal intercepts o...

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  20. A line through the variable point A(k+1,2k) meets the lines 7x+y-16=0,...

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