Find the coordina

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.

Here, a = BC = 39, b = CA = 56 and c = AB = 25

Also, x₁, y₁ = A (20, 15), x₂, y_{2 =} B (0, 0) and x₃, y₃ = C (−36, 15)

AND incentre

Hence, coordinate of incenter and centroid are ( - 1, 8)