Question

Consider three points

              ,

               and

              , then

Solution

Correct option is

P, Q, R are non-collinear

             

          

       

   

But if T be the point which divides PQ in the ratio  then

         

From above it is clear R does not lie on PQ and hence P, Q and R are non-collinear.

 

SIMILAR QUESTIONS

Q1

If a vertex of a triangle is (1, 1) and the mid-point of two sides through the vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

Q2

If the equation of the locus of a point equidistant from the points

(a1b1) and (a2b2) is (a1 – a1)x + (b1  –  b2)y + c = 0,

Then the value of c is :

Q3

The line joining the point  is produced to the point L(x, y) so that AL : LB b : a, then 

               

Q4

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If and I be the centoid and in center of the triangle, then GI is equal to

Q5

If a, b, c are relation by 4a2 + 9b2 – 9c2 + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

Q6

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the numbers of integral coordinates strictly inside the triangle (integral coordinates of both and y)

Q7

If x1x2x3 as well as y1y2y3 are in G.P. with the same common ratio, then the points (x1y1), (x2y2) and (x3y3)

Q8

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

Q9

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

Q10

The lines p(p2 + 1)x – y + q = 0 and (p2 + 1)2 x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for