Q. 144.8( 6 Votes )
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 :
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, y2 = B (0, 0) and x3, y3 = C (−36, 15)
AND incentre 
Hence, coordinate of incenter and centroid are 
( - 1, 8)
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and 
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