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If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24?
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If a,b,c are not equal to each other then prove that the points( a,a s...
You can prove this three points aren't collinear by contradicting the statement, that is by trying to prove the collinearity. firstly name the points A,B and C. Now find the value of AB,BC and CA.If not then then the there points aren't collinear.
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If a,b,c are not equal to each other then prove that the points( a,a s...
Proof by contradiction:
Assumption:
The points (a, a^2), (b, b^2), and (c, c^2) are collinear.
Explanation:
To prove that the points are not collinear, we assume the opposite and show that it leads to a contradiction.
Definition of collinear points:
Three points are collinear if and only if the slope between any two points is the same.
Defining the slope:
The slope between two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Calculating the slope between (a, a^2) and (b, b^2):
slope1 = (b^2 - a^2) / (b - a)
Calculating the slope between (b, b^2) and (c, c^2):
slope2 = (c^2 - b^2) / (c - b)
Assuming the points are collinear:
Since the points are collinear, slope1 = slope2.
Substituting the values:
(b^2 - a^2) / (b - a) = (c^2 - b^2) / (c - b)
Simplifying the equation:
(b + a) / (b - a) = (c + b) / (c - b)
Cross-multiplying:
(c - b)(b + a) = (b - a)(c + b)
Expanding:
cb + ca - b^2 - ab = bc + b^2 - ac - ab
Simplifying:
cb + ca - b^2 - ab = bc + b^2 - ac - ab
2ab + ca = 2bc + ca
2ab = 2bc
ab = bc
Contradiction:
Since a, b, and c are not equal, we can divide both sides of the equation by b to get:
a = c
This contradicts the assumption that a, b, and c are not equal to each other.
Hence, the points (a, a^2), (b, b^2), and (c, c^2) can never be collinear.
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If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24?
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If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24?.
If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a,b,c are not equal to each other then prove that the points( a,a square )(b, b square and (c, c square) can never be collinear 24?.
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