Q19 of 50 Page 220

The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4). Find its vertices. Also find the centriod of the triangle.

Given; The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4).

Let he vertices be A(x1, y1, z1), B(x2, y2, z2) and A(x3, y3, z3) respectively.



⇒ x1 =2-x2, y1 =10-y2, z1 =-2- z2



⇒ x3 =-x2 , y3 =8-y2 , z3 =-4-z2




∴ x2 = −1,


y2 = 6,


z2 = −7.


∴ x1 = 2 − x2 = 3,


y1 = 10 − y2 = 4,


z1 = −4 – z2 = 5.


∴ x3 = – x2 = 1,


y3 = 8 – y2 = 2,


z3 = −4 − z2 = 3.


∴ A(−1, 6, −7), B(3, 4, 5), C(1, 2, 3) are the required vertices.


Centroid of a triangle is given by the average of the coordinates of its vertices or midpoint of sides.


Centroid is


More from this chapter

All 50 →
17

Let A (2, 2, – 3), B (5, 6, 9) and C (2, 7, 9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D. Find the coordinates of D.

 18

Show that the three points A (2, 3, 4), B (–1, 2, – 3) and C (– 4, 1, – 10) are collinear and find the ratio in which C divides AB.

 20

Prove that the points (0, – 1, – 7), (2, 1, – 9) and (6, 5, – 13) are collinear. Find the ratio in which the first point divides the join of the other two.

 21

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin, coincides with the positive direction of the axes through the origin?