# NCERT Class 11-Math's: Chapter –12 Introduction to Three Dimensional Geometry Part 8

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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:**