# NCERT Class 11-Math՚S: Chapter – 12 Introduction to Three Dimensional Geometry Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 8:

Show that the point , and are collinear.

Answer:

Given; The point , and .

Points A, B and C are collinear.

Question 9:

Three consecutive vertices of a parallelogram ABCD are , , . Find the coordinates of the fourth vertex.

[Hint: Diagonals of a parallelogram have the same mid-point.]

Answer:

Question 10:

Show that the triangle ABC with vertices , and is right angled.

Answer:

Given; The vertices

Triangle ABC a right angled.

Question 11:

Find the centroid of a triangle, the mid-point of whose sides are , and .

Answer:

Question 12:

Find the centroid of a triangle, the mid-point of whose sides are and .

Answer:

Question 13:

The mid-points of the sides of a triangle are and . Find its vertices.

Answer:

Question 14:

Three vertices of a Parallelogram ABCD are , B and . Find the fourth vertex .

Answer:

Question 15:

Find the coordinate of the points which trisect the line segment joining the points and .

Answer:

Question 16:

If the origin is the centriod of a triangle ABC having vertices and , find the values of .

Answer:

Question 17:

Let , and be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D. Find the coordinates of D.

Answer: