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Find the value of ‘k’, if the point (0, 2) is equidistant from the points (3, k) and (k, 5)
- a)1
- b)– 1
- c)0
- d)2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the value of ‘k’, if the point (0, 2) is equidistant ...
Explanation:
Let point C (0, 2) is equidistant fromthe points A(3,k) and B(k,5).
Most Upvoted Answer
Find the value of ‘k’, if the point (0, 2) is equidistant ...
Understanding the Problem
To find the value of k such that the point (0, 2) is equidistant from the points (3, k) and (k, 5), we need to set up an equation based on the distance formula.
Distance Formula
The distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
Calculating Distances
1. Distance from (0, 2) to (3, k):
- Distance = √((3 - 0)² + (k - 2)²)
- This simplifies to:
- √(9 + (k - 2)²)
2. Distance from (0, 2) to (k, 5):
- Distance = √((k - 0)² + (5 - 2)²)
- This simplifies to:
- √(k² + 9)
Setting the Distances Equal
Since the point (0, 2) is equidistant from both points, we can set the two distances equal to each other:
√(9 + (k - 2)²) = √(k² + 9)
Squaring Both Sides
To eliminate the square roots, we square both sides:
9 + (k - 2)² = k² + 9
Simplifying the Equation
1. Remove 9 from both sides:
- (k - 2)² = k²
2. Expanding (k - 2)²:
- k² - 4k + 4 = k²
3. Subtracting k² from both sides:
- -4k + 4 = 0
4. Solving for k:
- 4k = 4
- k = 1
Conclusion
The value of k is 1. Thus, the correct answer is option 'A'.
To find the value of k such that the point (0, 2) is equidistant from the points (3, k) and (k, 5), we need to set up an equation based on the distance formula.
Distance Formula
The distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
Calculating Distances
1. Distance from (0, 2) to (3, k):
- Distance = √((3 - 0)² + (k - 2)²)
- This simplifies to:
- √(9 + (k - 2)²)
2. Distance from (0, 2) to (k, 5):
- Distance = √((k - 0)² + (5 - 2)²)
- This simplifies to:
- √(k² + 9)
Setting the Distances Equal
Since the point (0, 2) is equidistant from both points, we can set the two distances equal to each other:
√(9 + (k - 2)²) = √(k² + 9)
Squaring Both Sides
To eliminate the square roots, we square both sides:
9 + (k - 2)² = k² + 9
Simplifying the Equation
1. Remove 9 from both sides:
- (k - 2)² = k²
2. Expanding (k - 2)²:
- k² - 4k + 4 = k²
3. Subtracting k² from both sides:
- -4k + 4 = 0
4. Solving for k:
- 4k = 4
- k = 1
Conclusion
The value of k is 1. Thus, the correct answer is option 'A'.
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Find the value of ‘k’, if the point (0, 2) is equidistant from the points (3, k) and (k, 5)a)1b)– 1c)0d)2Correct answer is option 'A'. Can you explain this answer?
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