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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2.
Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Directions: In the following questions, A statement of Assertion (A) ...
Consider the given points.
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(−k + 1, 2k), (k, 2 − 2k),(−4 −k, 6 − 2k)
Since, these points are collinear. Therefore the area of triangle formed by the triangle formed by the points will be zero.
Therefore,
(−k + 1)(2 − 2k − 6 + 2k) + k(6 − 2k − 2k) + (−4 − k)(2k − 2 + 2k) = 0
(−k + 1)(−4) + k(6 − 4k) + (−4 − k)(4k − 2) = 0
4k − 4 + 6k − 4k2 − 16k + 8 − 4k2 + 2k = 0
−2k2 − k + 1 = 0
2k2 + k − 1 = 0
2k2 + 2k − k − 1 = 0
2k(k + 1) − 1(k + 1) = 0
(k + 1)(2k − 1) = 0
k = −1 or k = 1/2.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion: The points (k, 2 - 2k), (-k 1, 2k), and (-4 - k, 6 - 2k) are collinear if k = 1/2.
Reason: Three points A, B, and C are collinear in the same straight line if AB × BC = AC.
To prove that the given points are collinear, we need to check if the product of the slopes of the line segments formed by these points is equal to 1.
Let's calculate the slopes of the line segments AB, BC, and AC.
Line segment AB:
Coordinates of A: (k, 2 - 2k)
Coordinates of B: (-k 1, 2k)
The slope of AB (m1) = (2k - (2 - 2k))/(-k - k) = (4k - 2)/(-2k) = -2/k
Line segment BC:
Coordinates of B: (-k 1, 2k)
Coordinates of C: (-4 - k, 6 - 2k)
The slope of BC (m2) = (6 - 2k - 2k)/(-4 - k - (-k 1)) = (6 - 4k)/(-3 - k) = 2(2 - k)/(k + 3)
Line segment AC:
Coordinates of A: (k, 2 - 2k)
Coordinates of C: (-4 - k, 6 - 2k)
The slope of AC (m3) = (6 - 2k - (2 - 2k))/(-4 - k - k) = (6 - 4k)/(-3 - k) = 2(2 - k)/(k + 3)
Now, let's check if AB × BC = AC.
AB × BC = (-2/k) × (2(2 - k)/(k + 3)) = -4(2 - k)/(k(k + 3))
AC = 2(2 - k)/(k + 3)
To check if AB × BC = AC, we need to simplify the expressions and see if they are equal.
-4(2 - k)/(k(k + 3)) = 2(2 - k)/(k + 3)
Simplifying both sides:
-8 + 4k = 4 - 2k
6k = 12
k = 2
Since the value of k is not equal to 1/2, the given points are not collinear.
Therefore, both the assertion and reason are true, but the reason is not the correct explanation of the assertion.
Reason: Three points A, B, and C are collinear in the same straight line if AB × BC = AC.
To prove that the given points are collinear, we need to check if the product of the slopes of the line segments formed by these points is equal to 1.
Let's calculate the slopes of the line segments AB, BC, and AC.
Line segment AB:
Coordinates of A: (k, 2 - 2k)
Coordinates of B: (-k 1, 2k)
The slope of AB (m1) = (2k - (2 - 2k))/(-k - k) = (4k - 2)/(-2k) = -2/k
Line segment BC:
Coordinates of B: (-k 1, 2k)
Coordinates of C: (-4 - k, 6 - 2k)
The slope of BC (m2) = (6 - 2k - 2k)/(-4 - k - (-k 1)) = (6 - 4k)/(-3 - k) = 2(2 - k)/(k + 3)
Line segment AC:
Coordinates of A: (k, 2 - 2k)
Coordinates of C: (-4 - k, 6 - 2k)
The slope of AC (m3) = (6 - 2k - (2 - 2k))/(-4 - k - k) = (6 - 4k)/(-3 - k) = 2(2 - k)/(k + 3)
Now, let's check if AB × BC = AC.
AB × BC = (-2/k) × (2(2 - k)/(k + 3)) = -4(2 - k)/(k(k + 3))
AC = 2(2 - k)/(k + 3)
To check if AB × BC = AC, we need to simplify the expressions and see if they are equal.
-4(2 - k)/(k(k + 3)) = 2(2 - k)/(k + 3)
Simplifying both sides:
-8 + 4k = 4 - 2k
6k = 12
k = 2
Since the value of k is not equal to 1/2, the given points are not collinear.
Therefore, both the assertion and reason are true, but the reason is not the correct explanation of the assertion.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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