Question

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

Solution

Correct option is

(3, – 9)

Let the co –ordinates of the required point be P(xy).

i.e.,                 = 3 and = – 9

Hence the required point is (3, – 9).

 

SIMILAR QUESTIONS

Q1

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

Consider the point   then

Q8

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

Q9

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.

Q10

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