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If coordinates of vertices of a triangle are (7, 6, 4), (5, 4, 6), (9, 5, 8), find the coordinates of centroid of the triangle.

Correct Answer: (7, 5, 3)
If coordinates of vertices of a triangle are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) the coordinates of centroid of the triangle are ((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3) So, coordinates of centroid of the given triangle are ((7+5+9)/3, (6+4+5)/3, (4+6+8)/3) = (7, 5, 3).

Consider the following statements :I. Every equilateral triangle is necessarily an isosceles triangle.II. Every right-angled triangle is necessarily an isosceles triangle.III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle.The correct statements are:

An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?

With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates; (x1, y1) = (1, 0);(x2, y2) = (2, 2); (x3, y3) = (4, 3). The area of the triangle is equal to

What are the co­ordinates of the centroid of a triangle, whose vertices are A(­2,­5), B(4,­4) and C(7,3)?

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In a triangle, the distance of the centroid from the three vertices is 4cm, 6cm and 8cm respectively. Then the length of the smallest median is:

What are the co-ordinates of the centroid of a triangle, whose vertices are A(2 , 5), B(-4 , 0) and C(5 , 4)?

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?

What are the co-ordinates of the centroid of a triangle, whose vertices are A(-2,5), B(3,-2) and C(5,3)?