Home
Class 12
MATHS
The vertices of a triangle are (1, a), (...

The vertices of a triangle are `(1, a), (2, b) and (c^2, -3).` (i) Prove that its centroid can not lie on the y-axis. (ii) Find the condition that the centroid may lie on the x-axis for any value of `a, b, c in RR.`

Text Solution

Verified by Experts

The correct Answer is:
`a+b=3`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|1 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

Similar Questions

Explore conceptually related problems

The vertices of a triangle are (1, a), (2, b) and (c^(2)-3) Find the condition that the centroid may lie on the X-axis.

The vertices of a triangle are A (-2, 1), B (6, -2) and C (4, 3). Find the lengths of the altitudes of the triangle.

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

The centroid of the triangle with vertices (1, sqrt(3)), (0, 0) and (2, 0) is

Two vertices of a traingle are (2,-6,4) and (4,-2,3) and its centroid is (8/3,-1,3) . Find the third vertex.

The vertices of a triangle are (1, 2), (h, -3) and (-4, k). Find the value of sqrt({(h+k)^(2)+(h+3k)^(2)}) . If the centroid of the triangle be at point (5, -1).

Find the coordinates of the centroid of the triangle whose vertex are (1,-2),(3,2)and (-1,0).

Let A(4, 2), B (6, 5) and C (1, 4) be the vertices of triangleABC . :- If (x_1,y_1) , B (x_2,y_2) and C (x_3,y_3) the vertices of triangleABC , find the coordinates of the centroid of the triangle.

The vertices of a triangle an A(1,2), B(-1,3) and C(3, 4). Let D, E, F divide BC, CA, AB respectively in the same ratio. Statement I : The centroid of triangle DEF is (1, 3). Statement II : The triangle ABC and DEF have the same centroid.

If A (2, -3) and B (-2, 1) are two vertices of a triangle and third vertex moves on the line 2x + 3y = 9, then the locus of the centroid of the triangle is :