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What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?
- a)2x + 4y -11= 0
- b)2x -4y -5 = 0
- c)2x - 4y - 11 = 0
- d)x - y + 1 = 0
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the equation of the right bisector of the line segment joining...
Equation of given line is
and slope of perpendicular = 
The perpendicular is also bisector, therefore it will pass through its mid-point.
=> Coordinates o f m id-point of given line are :
So, equation of perpendicular bisector is :
Most Upvoted Answer
What is the equation of the right bisector of the line segment joining...
To find the equation of the right bisector of the line segment joining (1,1) and (2,3), we can follow these steps:
Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint (x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Given points: (1,1) and (2,3)
Midpoint (x, y) = ((1 + 2)/2, (1 + 3)/2)
Midpoint (x, y) = (3/2, 4/2)
Midpoint (x, y) = (3/2, 2)
Step 2: Find the slope of the line segment.
The slope formula is given by:
Slope (m) = (y2 - y1)/(x2 - x1)
Given points: (1,1) and (2,3)
Slope (m) = (3 - 1)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
Step 3: Find the negative reciprocal of the slope.
The negative reciprocal of a slope is obtained by flipping the fraction and changing the sign.
Negative reciprocal = -1/2
Step 4: Find the equation of the line using the midpoint and the negative reciprocal of the slope.
The equation of a line in slope-intercept form is given by:
y - y1 = m(x - x1)
Using the midpoint (3/2, 2) and the negative reciprocal of the slope (-1/2), we have:
y - 2 = (-1/2)(x - 3/2)
Step 5: Simplify the equation to obtain the final answer.
Multiply through by -2 to remove the fraction:
-2(y - 2) = -2(-1/2)(x - 3/2)
-2y + 4 = 1(x - 3/2)
Simplifying further:
-2y + 4 = x - 3/2
x - 2y - 4 + 3/2 = 0
x - 2y - 5/2 = 0
Comparing this equation with the given options, we can see that the correct answer is option 'B':
2x - 4y - 5 = 0
Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint (x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Given points: (1,1) and (2,3)
Midpoint (x, y) = ((1 + 2)/2, (1 + 3)/2)
Midpoint (x, y) = (3/2, 4/2)
Midpoint (x, y) = (3/2, 2)
Step 2: Find the slope of the line segment.
The slope formula is given by:
Slope (m) = (y2 - y1)/(x2 - x1)
Given points: (1,1) and (2,3)
Slope (m) = (3 - 1)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
Step 3: Find the negative reciprocal of the slope.
The negative reciprocal of a slope is obtained by flipping the fraction and changing the sign.
Negative reciprocal = -1/2
Step 4: Find the equation of the line using the midpoint and the negative reciprocal of the slope.
The equation of a line in slope-intercept form is given by:
y - y1 = m(x - x1)
Using the midpoint (3/2, 2) and the negative reciprocal of the slope (-1/2), we have:
y - 2 = (-1/2)(x - 3/2)
Step 5: Simplify the equation to obtain the final answer.
Multiply through by -2 to remove the fraction:
-2(y - 2) = -2(-1/2)(x - 3/2)
-2y + 4 = 1(x - 3/2)
Simplifying further:
-2y + 4 = x - 3/2
x - 2y - 4 + 3/2 = 0
x - 2y - 5/2 = 0
Comparing this equation with the given options, we can see that the correct answer is option 'B':
2x - 4y - 5 = 0
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What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer?
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What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer?.
What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the equation of the right bisector of the line segment joining (1,1) and (2,3)?a)2x + 4y -11= 0b)2x -4y -5 = 0c)2x - 4y - 11= 0d)x - y + 1 = 0Correct answer is option 'A'. Can you explain this answer?.
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