Equation of line Solution5



In this page equation of line solution5 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(10) By using the concept of the equation of the straight line,prove that the given three points are collinear.

(i)  (4,2) (7,5) and (9,7)

Solution:

To verify the three given points are collinear we have to find equation of the line using any two points and have to apply the remaining point in the previous equation. If the equation got satisfied then we can decide the given three points are collinear otherwise we can say the given points are not collinear.

Equation of the line:

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - 2)/(5 - 2) = (x - 4)/(7 - 4)

(y - 2)/3 = (x - 4)/3

(y - 2) =  (x - 4)

x - y -4 + 2 = 0

x - y - 2 = 0

Now we have to apply the remaining point that is (9 ,7) in the given equation

9 - 7 - 2 = 0

9 - 9 = 0

 0 = 0

Therefore we can say the given points are collinear


(ii)  (1,4) (3,-2) and (-3,16)

Solution:

To verify the three given points are collinear we have to find equation of the line using any two points and have to apply the remaining point in the previous equation. If the equation got satisfied then we can decide the given three points are collinear otherwise we can say the given points are not collinear.

Equation of the line:

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(1,4) (3,-2)

(y - 4)/(-2 - 4) = (x - 1)/(3 - 1)

(y - 4)/(-6) = (x - 1)/2

2(y - 4) =  -6 (x - 1)

2 y - 8 = - 6x + 6

6 x + 2 y - 6 - 8 = 0

6 x + 2 y - 14 = 0

Divide the whole equation by 2 we get,

3 x + y - 7 = 0

Now we have to apply the remaining point that is (-3 ,16) in the given equation

3(-3) + 16 - 7 = 0

-9 + 16 - 7 = 0

 -16 + 16  = 0

 0 = 0

Therefore we can say the given points are collinear   

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