show that the following sets of points are collinear and find the equation of the line L containing them 1) (-5,1),(5,5),(10,7) 2) (1,3), (-2,-6),(2,6) 3) (a,b+c),(b,c+a),(c,a+b)
Answers
Step-by-step explanation:
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Given : sets of points
1) (-5,1),(5,5),(10,7)
2) (1,3), (-2,-6),(2,6)
3) (a,b+c),(b,c+a),(c,a+b)
To Find : Show that they are colinear
find the equation of the line containing them
Solution:
3 points are collinear if slope of any two pair of points is same.
1) (-5,1),(5,5),(10,7)
Slope = (5 - 1)/(5 - (-5)) = 4/10 = 2/5
Slope = ( 7 - 5)/(10 - 5) = 2/5
Equation of line
y - 5 = (2/5)(x - 5)
=> 5y - 25 = 2x - 10
=> 5y = 2x + 15
2) (1,3), (-2,-6),(2,6)
Similarly
slope = 3
Equation of line
y - 3 = 3(x - 1)
=> y = 3x
3) (a,b+c),(b,c+a),(c,a+b)
Slope = -1
Equation of line
y - b - c = -1(x - a)
=> x + y = a + b + c
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