Question

Find the coordinates of the incentre and centroid of the triangle whose sides have the equations 3x – 4y = 0, 12y + 5x = 0 and y – 15 = 0.

Answer 1

Given: lines are as follows: 

3x − 4y = 0 … (1) 

12y + 5x = 0 … (2) 

y − 15 = 0 … (3) 

Assuming: 

In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively. 

Concept Used: 

Point of intersection of two lines.

Explanation:

Solving (1) and (2): 

x = 0, y = 0 

Thus, AB and BC intersect at B (0, 0). 

Solving (1) and (3): 

x = 20 , y = 15 

Thus, AB and CA intersect at A (20, 15). 

Solving (2) and (3): x = −36 , y = 15 

Thus, BC and CA intersect at C (−36, 15). 

Let us find the lengths of sides AB, BC and CA.

Hence, coordinate of incenter and centroid are \(\Big(-\frac{16}{3},10\Big)\) and (-1,8)