# 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**: