Find the centroid and area of the triangle formed by
the following lines .
2y^2-xy-6x^2=0 , x+y+4=0
Answers
Answer:
Step-by-step explanation:
A detailed step-by-step explanation is provided in the attached photos.
Centroid is ( 20/9 , -44/9) , Area of triangle = 56/3 sq units of the triangle formed by 2y²-xy-6x²=0 , x+y+4=0
Given :
- Triangle formed by the lines 2y² - xy - 6x² = 0, , x+y+4=0
To Find :
- Centroid
- Area of the triangle
Solution:
Step 1:
Find Equation of lines from pair of lines
2y² - xy - 6x² =0
=> 2y² -4xy+ 3xy - 6x² = 0
=> 2y(y - 2x)+ 3x(y - 2x) = 0
=> (y - 2x)(2y + 3x) = 0
y - 2x = 0
2y + 3x = 0
Step 2:
Find coordinates of intersection of lines
y - 2x = 0 , 2y + 3x = 0
=> ( 0 , 0)
y - 2x = 0 , x+y+4=0
=> (-4/3 , -8/3)
x+y+4=0 , 2y + 3x = 0
=> (8 , -12)
Step 3:
Find centroid
( 0 , 0) , (-4/3 , -8/3) , (8 , -12)
= ( 0 - 4/3 + 8)/3 , (0 -8/3 - 12)/3
= ( 20/9 , -44/9)
centroid is ( 20/9 , -44/9)
Step 4:
Find Area of triangle
= (1/2) | 0 (-8/3 - (-12)) +(-4/3)(-12 - 0) + 8(0 - (-8/3)) |
= (1/2) |0 + 48/3+ 64/3 |
= (1/2) |112/3 |
= 56/3
Area of triangle = 56/3 sq units
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