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Show that the points `(a , a),(-a ,-a)` and `(-sqrt(3)a ,sqrt(3)a)` are the vertices of an equilateral triangle. Also, find its area.

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The correct Answer is:
`2sqrt3a^(2)` square units
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NAGEEN PRAKASHAN ENGLISH-CO-ORDINATE GEOMETRY-Exercise 7d
  1. Find the values of y of which the distance beween the points A(3,-1)an...

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  2. Find the relation between x and y such that the point P (x,y) is equid...

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  3. Find the point on Y-axis which is equidistant from the points (-5,2)an...

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  4. Find the co-ordinates of the point equidistant from three given points...

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  5. Show that the points (a , a),(-a ,-a) and (-sqrt(3)a ,sqrt(3)a) are th...

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  6. Show that the points (1,1),(-1,5),(7,9)and(9,5) taken in that order, ...

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  7. Show that the points A(3,5),B(6,0), C(1,-3) and D(-2,2) are the vertic...

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  8. If P(2,\ -1),\ \ Q(3,\ 4),\ \ R(-2,\ 3) and S(-3,\ -2) be four poin...

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  9. Find the co-ordinates of a point P on the line segment joining A(1,2)a...

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  10. Point P divides the line segment joining the points A(2,\ 1) and B(...

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  11. Find the ratio in which the point P (11,y) divides the line segment jo...

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  12. Two vertices of a DeltaABC are given by A(6,4)and B(-2,2) and its cent...

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  13. The base QR of an equilateral triangle PQR lies on X-axis. The co-ordi...

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  14. The mid-point P of the line segment joining the points A(-10 ,4)a n dB...

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  15. Find the value of k so that the area of the triangle with vertices (1,...

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  16. If A(4,-6),B(3,-2)and C(5,2) are the vertices of a DeltaABC and AD is ...

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  17. Find the area of quadrilateral ABCD, whose vertices are A(-4,8),B(-3,-...

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  18. If the area of DeltaABC with vertices A(x,y),B(1,2)and C(2,1) is 6 squ...

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