Question

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Solution

Correct option is

(–4, –15)

Let the third vertex be (xy) then the co – ordinates of the centroid of triangle are

                      

or          = – 4 and = – 15

Hence the third vertex is (–4, –15).

SIMILAR QUESTIONS

Q1

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

Q2

If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is

Q3

If α, β, γ are the real roots of the equation x3 – 3px3 + 3qx – 1 = 0, then the centroid of the triangle with vertices 

Q4

The number of points (p, q) such that p, q Ïµ {1, 2, 3, 4} and the equation px2 + qx + 1 = 0 has real roots is

Q5

If G is the centroid and I the incentre of the triangle with vertices A(–36, 7), B(20, 7) and C(0, –8), then GI is equal to

Q6

Consider the point   then

Q7

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q8

Find the co – ordinates of the point which divides the line segment joining the pints (5, – 2) and (9, 6) in the ratio 3 : 1.

Q9

Find the co – ordinates of a point which divides externally the line joining (1, 3) and (3, 9) in the ratio 1 : 3.

Q10

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).