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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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear 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 'B'. Can you explain this answer?
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Verified Answer
Directions: In the following questions, A statement of Assertion (A) ...
We know that the three points A,B and C are collinear if AB + BC = AC
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So, Reason is correct.
Let the ratio is k : 1. Here, x1 = -3, y1 = 10, x2 = 6, y2 = -8, x = -1, y = 6
Now, y-coordinate
⇒ -8k + 10 = 6k + 6
⇒ 10 – 6 = 6k + 8k
⇒ 14k = 4
⇒ k = 4/14 = 2/7
So, Assertion is correct
But reason (R) is not the correct explanation of assertion (A).
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Directions: In the following questions, A statement of Assertion (A) ...
Assertion and Reasoning
Assertion : The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear if AB BC = AC
Explanation
The given problem can be solved using section formula. The section formula gives the coordinates of a point which divides a line segment joining two given points in a given ratio. The coordinates of the point which divides the line segment joining (-3, 10) and (6, -8) internally in the ratio 2 : 7 can be found using the section formula as follows:
Let the point dividing the line segment in the given ratio be (x, y)
Then, using section formula,
x = [7(-3) + 2(6)] / (7 + 2) = -1
y = [7(10) + 2(-8)] / (7 + 2) = 6
Therefore, the point dividing the line segment joining (-3, 10) and (6, -8) internally in the ratio 2 : 7 is (-1, 6).
Hence, the assertion is true.
Now, let us verify the reason given in the problem.
The reason given in the problem states that three points A, B and C are collinear if AB BC = AC.
Using the distance formula, we can calculate the distances between the three given points as follows:
AB = √[(6 - (-3))^2 + (-8 - 10)^2] = √(81 + 324) = 15
BC = √[(-1 - 6)^2 + (6 - (-8))^2] = √(49 + 196) = 15
AC = √[(6 - (-3))^2 + (-8 - (-10))^2] = √(81 + 4) = √85
Now, AB + BC = 15 + 15 = 30, which is equal to AC = √85
Therefore, the given points are collinear.
Hence, the reason is also true.
However, the reason does not explain the assertion.
Therefore, option B is the correct choice.
Conclusion
The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally. Three points A, B and C are collinear if AB BC = AC. The assertion is true and the reason is also true but it does not explain the assertion. The correct option is B.
Assertion : The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear if AB BC = AC
Explanation
The given problem can be solved using section formula. The section formula gives the coordinates of a point which divides a line segment joining two given points in a given ratio. The coordinates of the point which divides the line segment joining (-3, 10) and (6, -8) internally in the ratio 2 : 7 can be found using the section formula as follows:
Let the point dividing the line segment in the given ratio be (x, y)
Then, using section formula,
x = [7(-3) + 2(6)] / (7 + 2) = -1
y = [7(10) + 2(-8)] / (7 + 2) = 6
Therefore, the point dividing the line segment joining (-3, 10) and (6, -8) internally in the ratio 2 : 7 is (-1, 6).
Hence, the assertion is true.
Now, let us verify the reason given in the problem.
The reason given in the problem states that three points A, B and C are collinear if AB BC = AC.
Using the distance formula, we can calculate the distances between the three given points as follows:
AB = √[(6 - (-3))^2 + (-8 - 10)^2] = √(81 + 324) = 15
BC = √[(-1 - 6)^2 + (6 - (-8))^2] = √(49 + 196) = 15
AC = √[(6 - (-3))^2 + (-8 - (-10))^2] = √(81 + 4) = √85
Now, AB + BC = 15 + 15 = 30, which is equal to AC = √85
Therefore, the given points are collinear.
Hence, the reason is also true.
However, the reason does not explain the assertion.
Therefore, option B is the correct choice.
Conclusion
The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally. Three points A, B and C are collinear if AB BC = AC. The assertion is true and the reason is also true but it does not explain the assertion. The correct option is B.
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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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. 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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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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 point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.Reason : Three points A,B and C are collinear if AB + BC = ACa)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 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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