Q. 144.8( 6 Votes )

Find the coordina

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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