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If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ is
- a)1
- b)0
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the points (2, 3), (4, k) and (6, – 3) are collinear, then th...
Explanation:
Let the points A (2, 3), B(4,k) and C(6,−3) be collinear.
If the points are collinear then area of triangle ABC formed by these three points is 0.
If the points are collinear then area of triangle ABC formed by these three points is 0.
Most Upvoted Answer
If the points (2, 3), (4, k) and (6, – 3) are collinear, then th...
Given information:
Three points (2, 3), (4, k), and (6, 3) are collinear.
Explanation:
To determine the value of k, we need to use the concept of collinearity. Collinearity means that the three points lie on the same straight line. In other words, the slope between any two points should be the same.
Step 1: Find the slope:
To find the slope between two points (x1, y1) and (x2, y2), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (2, 3) and (4, k), the slope is:
slope1 = (k - 3) / (4 - 2) = (k - 3) / 2
Using the points (4, k) and (6, 3), the slope is:
slope2 = (3 - k) / (6 - 4) = (3 - k) / 2
Step 2: Set the slopes equal:
Since the three points are collinear, the slopes between any two points should be equal. So, we set the slopes equal to each other and solve for k:
(k - 3) / 2 = (3 - k) / 2
Step 3: Solve for k:
Cross-multiplying the equation, we have:
(k - 3) = (3 - k)
Simplifying the equation, we get:
k - 3 = 3 - k
Combining like terms, we obtain:
2k = 6
Dividing both sides of the equation by 2, we get:
k = 3
Conclusion:
Therefore, the value of k is 3. Hence, option 'C' is the correct answer.
Three points (2, 3), (4, k), and (6, 3) are collinear.
Explanation:
To determine the value of k, we need to use the concept of collinearity. Collinearity means that the three points lie on the same straight line. In other words, the slope between any two points should be the same.
Step 1: Find the slope:
To find the slope between two points (x1, y1) and (x2, y2), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (2, 3) and (4, k), the slope is:
slope1 = (k - 3) / (4 - 2) = (k - 3) / 2
Using the points (4, k) and (6, 3), the slope is:
slope2 = (3 - k) / (6 - 4) = (3 - k) / 2
Step 2: Set the slopes equal:
Since the three points are collinear, the slopes between any two points should be equal. So, we set the slopes equal to each other and solve for k:
(k - 3) / 2 = (3 - k) / 2
Step 3: Solve for k:
Cross-multiplying the equation, we have:
(k - 3) = (3 - k)
Simplifying the equation, we get:
k - 3 = 3 - k
Combining like terms, we obtain:
2k = 6
Dividing both sides of the equation by 2, we get:
k = 3
Conclusion:
Therefore, the value of k is 3. Hence, option 'C' is the correct answer.
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If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer?
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If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer?.
If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ isa)1b)0c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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