Q. 415.0( 1 Vote )

One vertex of the A. (–1, –1)

B. (2, 2)

C. (–2, –2)

D. (2, –2)

Answer :


Let ABC be an equilateral triangle with vertex A (a, b)


Let AD BC and let (p, q) be the coordinates of D


Given that the centroid P lies at the origin (0, 0).


We know that, the centroid of a triangle divides the median in the ratio 1: 2


Now, using the section formula, we get






a + 2p = 0 and b + 2q = 0 …(A)


a + 2p = b + 2q


2p – 2q = b – a


2(p – q) = b – a …(i)


It is given that BC = x + y – 2 = 0


Since, the above equation passes through (p, q)


p + q – 2 = 0 …(ii)



Now, we find the slope of line AP




and equation of line BC is


x + y – 2 = 0


y = - x + 2


y = (-1)x + 2


Since the above equation is in y = mx + b form.


So, slope of line BC is



Since, both the lines are perpendicular to each other.


mAP × mBC = -1



b = a


Putting the value of b = a in eq. (i), we get


2(p – q) = b – b


2(p – q) = 0


p = q


Now, putting the value p = q in eq. (ii), we get


p + p – 2 = 0


2p = 2


p = 1


q = 1 [ p = q]


Putting the value of p and q in eq. (A), we get


a + 2 × 1 = 0 and b + 2 × 1 = 0


a = -2 and b = -2


So, the coordinates of vertex A (a, b) is (-2, -2)


Hence, the correct option is (c)

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