Find the centroid and area of the triangle formed by the lines 3x2
- 4xy + y2
= 0, 2x - y = 6.
Answers
Given : triangle formed by the lines 3x² - 4xy + y² = 0, 2x - y = 6.
To Find :centroid and area of the triangle
Solution:
3x² - 4xy + y² =0
=> 3x² - 3xy - xy + y² = 0
=> 3x(x - y) - y(x - y ) = 0
=> (3x - y)(x - y) = 0
=> 3x - y = 0
x - y = 0
3x - y = 0 , x - y = 0
=> (0 , 0)
3x - y = 0 , 2x - y = 6.
=> ( - 6 , -18 )
x - y = 0 , 2x - y = 6.
=> ( 6 , 6)
(0 , 0) , ( - 6 , -18 ) , ( 6 , 6)
Centroid = ( 0 - 6 + 6)/3 , ( 0 - 18 + 6)/3
= ( 0 , - 4)
Area of triangle
= (1/2) | 0 (-18 - 6) + 6(0 - 6) + 6(0 - (-18)) |
= (1/2) | 0 - 36 + 108 |
= (1/2) | 72 |
= 36
Area of triangle = 36 sq units
Learn More:
find the area of triangle formed by the lines 3x+y-2=0,5x+2y-3=0,2x ...
https://brainly.in/question/11965745
Find the area of the triangle formed by the straight lines 2x - y - 5=0 ...
https://brainly.in/question/11710045
