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Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.
- a)2x – 3y – 2 = 0
- b)5x – 7y + 4 = 0
- c)3x – 2y – 2 = 0
- d)4x – 5y + 13 = 0
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the equation of line passing through the mid-point of line joinin...
Mid Point [(3+5)/2, (4+6)/2]
= [8/2, 10/2]
= (4,5)
Perpendicular to the equation : 2x + 3y - 5 = 10
3x - 2y + k = 0
3(4) - 2(5) + k = 0
12 - 10 + k 0
k = -2
Therefore the equation is : 3x - 2y - 2 = 0
= [8/2, 10/2]
= (4,5)
Perpendicular to the equation : 2x + 3y - 5 = 10
3x - 2y + k = 0
3(4) - 2(5) + k = 0
12 - 10 + k 0
k = -2
Therefore the equation is : 3x - 2y - 2 = 0
Most Upvoted Answer
Find the equation of line passing through the mid-point of line joinin...
Find the mid point as (4,5) then the equation of required line is 3(x-4)-2(y-5)=0>>>> 3x-2y-2=0
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Find the equation of line passing through the mid-point of line joinin...
To find the equation of a line passing through the midpoint of the line joining (3, 4) and (5, 6), we first need to find the coordinates of the midpoint.
The midpoint formula is given by:
(x₁ + x₂)/2 , (y₁ + y₂)/2
Using the coordinates (x₁, y₁) = (3, 4) and (x₂, y₂) = (5, 6), we can substitute these values into the formula:
(x + 3)/2 , (y + 4)/2
Simplifying this expression, we get:
(x + 3)/2 , (y + 4)/2 = (x + 3)/2 , (y + 4)/2
Now we need to find the slope of the line perpendicular to the equation 2x - 3y = 5. The slope of this line can be found by rearranging the equation in slope-intercept form (y = mx + b), where m is the slope:
2x - 3y = 5
-3y = -2x + 5
y = (2/3)x - 5/3
The slope of this line is 2/3. The slope of any line perpendicular to this line will be the negative reciprocal of 2/3, which is -3/2.
Now that we have the slope (-3/2) and the coordinates of the midpoint (x + 3)/2 , (y + 4)/2, we can use the point-slope form of a line to find the equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
Substituting the midpoint coordinates and the slope into this formula, we get:
y - (y + 4)/2 = (-3/2)(x - (x + 3)/2)
Simplifying this expression, we get:
2y - (y + 4) = -3(x - (x + 3)/2)
Multiplying through by 2 to eliminate the fraction, we get:
2(2y - (y + 4)) = -3(2x - (x + 3))
Expanding and simplifying, we get:
4y - 2y - 8 = -6x + 3
Combining like terms, we get:
2y - 8 = -6x + 3
Adding 6x to both sides, we get:
2y + 6x - 8 = 3
Adding 8 to both sides, we get:
2y + 6x = 11
Thus, the equation of the line passing through the midpoint of the line joining (3, 4) and (5, 6) and perpendicular to the equation 2x - 3y = 5 is 2y + 6x = 11.
The midpoint formula is given by:
(x₁ + x₂)/2 , (y₁ + y₂)/2
Using the coordinates (x₁, y₁) = (3, 4) and (x₂, y₂) = (5, 6), we can substitute these values into the formula:
(x + 3)/2 , (y + 4)/2
Simplifying this expression, we get:
(x + 3)/2 , (y + 4)/2 = (x + 3)/2 , (y + 4)/2
Now we need to find the slope of the line perpendicular to the equation 2x - 3y = 5. The slope of this line can be found by rearranging the equation in slope-intercept form (y = mx + b), where m is the slope:
2x - 3y = 5
-3y = -2x + 5
y = (2/3)x - 5/3
The slope of this line is 2/3. The slope of any line perpendicular to this line will be the negative reciprocal of 2/3, which is -3/2.
Now that we have the slope (-3/2) and the coordinates of the midpoint (x + 3)/2 , (y + 4)/2, we can use the point-slope form of a line to find the equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
Substituting the midpoint coordinates and the slope into this formula, we get:
y - (y + 4)/2 = (-3/2)(x - (x + 3)/2)
Simplifying this expression, we get:
2y - (y + 4) = -3(x - (x + 3)/2)
Multiplying through by 2 to eliminate the fraction, we get:
2(2y - (y + 4)) = -3(2x - (x + 3))
Expanding and simplifying, we get:
4y - 2y - 8 = -6x + 3
Combining like terms, we get:
2y - 8 = -6x + 3
Adding 6x to both sides, we get:
2y + 6x - 8 = 3
Adding 8 to both sides, we get:
2y + 6x = 11
Thus, the equation of the line passing through the midpoint of the line joining (3, 4) and (5, 6) and perpendicular to the equation 2x - 3y = 5 is 2y + 6x = 11.
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Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer?
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Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer?.
Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.a)2x – 3y – 2 = 0b)5x – 7y + 4 = 0c)3x – 2y – 2 = 0d)4x – 5y + 13 = 0Correct answer is option 'C'. Can you explain this answer?.
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