Question

If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is

(a) 183 sq. units

(b) $\frac{183}{2}$ sq. units

(c) 366 sq. units

(d) $\frac{183}{4}$ sq. units

Answer 1

We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be.

The co-ordinates of other two vertices are (4,−3) and (−9, 7)

The co-ordinate of the centroid is (1, 4)

We know that the co-ordinates of the centroid of a triangle whose vertices are is

So,

Compare individual terms on both the sides-

So,

Similarly,

So,

So the co-ordinate of third vertex is (8, 8)

In general if are non-collinear points then are of the triangle formed is given by-,

So,

So the answer is (b)