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Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is...
U need not to do much calculations here ...just simply go through the options . put the values of X and Y from the options in the given equation of line ...the option which will satisfy the equation will be ur ans .... I mean see... by putting 2nd option ..
LHS= 2 (4)-3 (1)=8-3 = 5 = RHS .....(satisfied)
hence B is ryt ..
LHS= 2 (4)-3 (1)=8-3 = 5 = RHS .....(satisfied)
hence B is ryt ..
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Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is...
Understanding the Problem
To find a point on the line 2x - 3y = 5 that is equidistant from the points (1, 2) and (3, 4), we need to break down the problem.
Step 1: Equation of the Line
The line is given by the equation:
- 2x - 3y = 5
Step 2: Distance Formula
The distance D between two points (x1, y1) and (x2, y2) is calculated as:
- D = √[(x2 - x1)² + (y2 - y1)²]
Step 3: Equidistant Condition
Let P(x, y) be the point on the line. We need:
- Distance from P to (1, 2) = Distance from P to (3, 4)
Step 4: Setting Up the Equation
Using the distance formula, we can set up the equation:
- √[(x - 1)² + (y - 2)²] = √[(x - 3)² + (y - 4)²]
Squaring both sides and simplifying will lead us to a relationship between x and y.
Step 5: Substitute the Line Equation
Since P lies on the line, we can express y in terms of x using the line equation:
- y = (2/3)x - (5/3)
Substituting this expression for y into the equidistant condition allows us to solve for x.
Step 6: Solving for Coordinates
After performing the algebra, we find that the coordinates satisfying both the line equation and the equidistant condition yield the point (4, 1).
Conclusion
Thus, the correct answer is:
- Option 'B': (4, 1)
This point is both on the line and equidistant from the given points.
To find a point on the line 2x - 3y = 5 that is equidistant from the points (1, 2) and (3, 4), we need to break down the problem.
Step 1: Equation of the Line
The line is given by the equation:
- 2x - 3y = 5
Step 2: Distance Formula
The distance D between two points (x1, y1) and (x2, y2) is calculated as:
- D = √[(x2 - x1)² + (y2 - y1)²]
Step 3: Equidistant Condition
Let P(x, y) be the point on the line. We need:
- Distance from P to (1, 2) = Distance from P to (3, 4)
Step 4: Setting Up the Equation
Using the distance formula, we can set up the equation:
- √[(x - 1)² + (y - 2)²] = √[(x - 3)² + (y - 4)²]
Squaring both sides and simplifying will lead us to a relationship between x and y.
Step 5: Substitute the Line Equation
Since P lies on the line, we can express y in terms of x using the line equation:
- y = (2/3)x - (5/3)
Substituting this expression for y into the equidistant condition allows us to solve for x.
Step 6: Solving for Coordinates
After performing the algebra, we find that the coordinates satisfying both the line equation and the equidistant condition yield the point (4, 1).
Conclusion
Thus, the correct answer is:
- Option 'B': (4, 1)
This point is both on the line and equidistant from the given points.
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Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer?
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Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer?.
Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Point on the line 2x - 3y = 5 equidistant from ( 1, 2 ) , ( 3 , 4 ) is a) ( 2, 3 ) b) ( 4, 1 ) c) ( 1, -1 ) d) (4, 6 ) Correct answer is option 'B'. Can you explain this answer?.
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