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An equilateral triangle has each side to...

An equilateral triangle has each side to a. If the coordinates of its vertices are `(x_(1), y_(1)), (x_(2), y_(2))` and `(x_(3), y_(3))` then the square of the determinat `|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2` equals

A

`3a^(4)`

B

`(3a^(4))/(2)`

C

`(3)/(4)a^(4)`

D

`(3)/(8)a^(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-COORDINATE SYSTEM AND COORDINATES -Exercise For Session 3
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  2. The incentre of the triangle whose vertices are (-36, 7), (20, 7) and ...

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  3. If the orthocentre and centroid of a triangle are (-3, 5) and (3, 3) t...

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  4. An equilateral triangle has each side to a. If the coordinates of its ...

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  5. The vertices of a triangle are A(0, 0), B(0, 2) and C(2, 0). The dista...

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  6. Area of the triangle with vertices (a, b), (x1,y1) and (x2, y2) where ...

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  7. The points (x +1, 2), (1, x +2), ((1)/(x+1),(2)/(x+1)) are collinear, ...

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  8. The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance...

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  9. The centroid of the triangle with vertices (1, sqrt(3)), (0, 0) and (2...

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  10. The vertices of a triangle are (0, 0), (1,0) and (0,1). Then excentre ...

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  11. If alpha, beta gamma are the real roots of the equation x^(3)-3px^(2)+...

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  12. If centroid of a triangle be (1, 4) and the coordinates of its any two...

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  13. Find the coordinates of the orthocentre of the triangle whose vertices...

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  14. Show that the area of the triangle with vertices (lambda, lambda-2), (...

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  15. Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

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  16. Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ...

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  17. If the points (x1, y1),(x2,y2), and (x3, y3) are collinear show that (...

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  18. The coordinates of points A,B,C and D are (-3, 5), (4, -2), (x, 3x) an...

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  19. Find the area of the hexagon whose consecutive vertices are (5, 0), (4...

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