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If the point (x, y) is equidistant from the points (5, 1) and ( – 1, 5), then the relation between ‘x’ and ‘y’ is given by
- a)3x = 2y
- b)– 2x = 3y
- c)2x = 3y
- d)3x = – 2y
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the point (x, y) is equidistant from the points (5, 1) and ( –...
Explanation:
Let the point C(x,y)is equidistant from the points A (5, 1) and B(−1,5).(−1,5).
i.e. AC = BC
Most Upvoted Answer
If the point (x, y) is equidistant from the points (5, 1) and ( –...
Given:
- The point (x, y) is equidistant from the points (5, 1) and (1, 5).
To find:
- The relation between x and y.
Explanation:
To find the relation between x and y, we need to find the distance between the point (x, y) and each of the given points. Let's calculate it step by step.
Step 1:
- Distance between the point (x, y) and (5, 1):
The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substituting the values, we have:
d₁ = √[(5 - x)² + (1 - y)²]
Step 2:
- Distance between the point (x, y) and (1, 5):
Similarly, using the distance formula, we have:
d₂ = √[(1 - x)² + (5 - y)²]
Step 3:
Since the point (x, y) is equidistant from both (5, 1) and (1, 5), we can set the distances equal to each other:
d₁ = d₂
Substituting the values of d₁ and d₂, we have:
√[(5 - x)² + (1 - y)²] = √[(1 - x)² + (5 - y)²]
Step 4:
To eliminate the square roots, we can square both sides of the equation:
[(5 - x)² + (1 - y)²] = [(1 - x)² + (5 - y)²]
Step 5:
Expanding both sides of the equation:
(25 - 10x + x² + 1 - 2y + y²) = (1 - 2x + x² + 25 - 10y + y²)
Step 6:
Simplifying the equation by combining like terms:
26 - 10x + x² - 2y + y² = 26 - 2x + x² - 10y + y²
Step 7:
Cancelling out the common terms on both sides, we get:
-10x - 2y = -2x - 10y
Step 8:
Rearranging the equation to isolate x and y terms:
-10x + 2x = -10y + 2y
Simplifying further:
-8x = -8y
Step 9:
Dividing both sides of the equation by -8, we get:
x = y
Conclusion:
The relation between x and y is given by:
x = y
Therefore, the correct answer is option 'A': 3x = 2y.
- The point (x, y) is equidistant from the points (5, 1) and (1, 5).
To find:
- The relation between x and y.
Explanation:
To find the relation between x and y, we need to find the distance between the point (x, y) and each of the given points. Let's calculate it step by step.
Step 1:
- Distance between the point (x, y) and (5, 1):
The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substituting the values, we have:
d₁ = √[(5 - x)² + (1 - y)²]
Step 2:
- Distance between the point (x, y) and (1, 5):
Similarly, using the distance formula, we have:
d₂ = √[(1 - x)² + (5 - y)²]
Step 3:
Since the point (x, y) is equidistant from both (5, 1) and (1, 5), we can set the distances equal to each other:
d₁ = d₂
Substituting the values of d₁ and d₂, we have:
√[(5 - x)² + (1 - y)²] = √[(1 - x)² + (5 - y)²]
Step 4:
To eliminate the square roots, we can square both sides of the equation:
[(5 - x)² + (1 - y)²] = [(1 - x)² + (5 - y)²]
Step 5:
Expanding both sides of the equation:
(25 - 10x + x² + 1 - 2y + y²) = (1 - 2x + x² + 25 - 10y + y²)
Step 6:
Simplifying the equation by combining like terms:
26 - 10x + x² - 2y + y² = 26 - 2x + x² - 10y + y²
Step 7:
Cancelling out the common terms on both sides, we get:
-10x - 2y = -2x - 10y
Step 8:
Rearranging the equation to isolate x and y terms:
-10x + 2x = -10y + 2y
Simplifying further:
-8x = -8y
Step 9:
Dividing both sides of the equation by -8, we get:
x = y
Conclusion:
The relation between x and y is given by:
x = y
Therefore, the correct answer is option 'A': 3x = 2y.
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Question Description
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