centroid of triangle the equations of whose sides are 12x2-20xy+7y2 and 2x-3y+4=0 is
Answers
Answer:
(8/3), (8/3)
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Step-by-step explanation:
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8/3 , 8/3 is centroid of triangle the equations of whose sides are 12x² - 20xy + 7y² = 0 and 2x-3y+4=0
Step-by-step explanation:
12x² - 20xy + 7y²
= 12x² - 6xy - 14xy + 7y²
= 6x(2x - y) - 7y(2x - y)
= (6x - 7y)(2x - y)
Sides are
6x - 7y = 0 Eq1
2x - y = 0 Eq2
2x - 3y + 4 = 0 Eq3
Eq1 - 3*Eq2
=> -7y + 3y = 0 => y = 0 & x = 0
(0 , 0)
Eq1 - 3 * Eq3
=> -7y + 9y - 12 = 0
=> 2y = 12
=> y = 6
x =7
(7 , 6)
Eq2 - Eq3
2y - 4 = 0
=> y = 2
x = 1
(1 , 2)
(0, 0) , (1,2) , (7 , 6)
Centroid = (0 + 1 + 7)/3 , (0+ 2 + 6)/3
= 8/3 , 8/3
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