Q23 of 184 Page 10

The area of a triangle is 3 square units. Two of its vertices are A(3,1), B(1,-3) and the centroid of the triangle lies on x-axis. Find the coordinates of the third vertex C.

Given: Coordinates of Triangle are A(3, 1) and B(1, -3)


Centroid of triangle lies on x- axis.


Let the third coordinate be C(x, y)


Centroid of the triangle with vertices (x1, y1), (x2, y2), (x3, y3) is given by,


C(X, Y)


The y coordinate of centroid will be 0, as it lies opn x – axis.


Therefore,


y1 + y2 + y3 = 0


1 – 3 + y3 = 0


y3 = 2


So, C(x, y) becomes (x, 2)


We are given that the area of triangle = 3 square units.


We know that,


Area of triangle


Putting the values we get,


3


-15 – 1 + 4x = 6


4x = 22



Hence, coordinates of the third vertex are


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