Question

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

Solution

Correct option is

Since Δ1 = Δ2 = Δ3 therefore R is the centroid of the triangle OPQ i.e. 

                                                                          

SIMILAR QUESTIONS

Q1

What will be the coordinates of the point in original position ifr its coordinates after rotation of axes through an angle 600  ?

Q2

The in centre of the triangle with vertices , (0, 0) and (2, 0) is

Q3

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

Q4

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 :

Q5

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

               

Q6

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

Q7

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:

Q8

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)

Q9

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

Q10

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