Q12 of 23 Page 330

The co-ordinates of centroid of triangle is (6, 9) and two vertices are (15, 0) and (0, 10); let us find the co-ordinates of third vertex.

Let the vertices of triangle be


A = (x1, y1) = (15, 0) and


B = (x2, y2) = (0, 10) and


C = (x3, y3)


Centroid G = (6, 9)


Centroid of a triangle is given by


G =


⇒ (6, 9) =


Substituting values


⇒ (6, 9) =


Equating x and y coordinates


⇒ = 6 and = 9


⇒ 15 + x3 = 18 and 10 + y3 = 27


⇒ x3 = 3 and y3 = 17


Hence the coordinates of third vertex is (3, 17)


More from this chapter

All 23 →
11

If in triangle ABC, the co-ordinates of vertex A is (7, –4) and centroid of triangle is (1, 2), then the co-ordinates a mid point of BC is

 12

The co-ordinates of mid-points of the sides of a triangle ABC are (0, 1), (1, 1) and (1, 0); let us find the co-ordinates of its centroid.

 12

If the three points (a, 0), (0, b) and (1, 1) are collinear then let us show that

12

Let us calculate the area of triangular region formed by the three points (1, 4), (–1, 2) and (–4, 1)