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The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is:
- a)(6, 3)
- b)(3, 6)
- c)(0, 0)
- d)(2, 5)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The point where the perpendicular bisector of the line segment joining...
Since, the point, where the perpendicular bisector of a line segment cuts, is the mid-point of that line segment.
∴ Coordinates of Mid-point of line segment AB =
∴ Coordinates of Mid-point of line segment AB =
Most Upvoted Answer
The point where the perpendicular bisector of the line segment joining...
Let the point be P.
Let the points be(x3,y3).
Given the line segment is perpendicular bisector.
Therefore P is the mid-point of line segment AB.
Using Mid-Point Formula,
x3=(x1+x2/2)=(2+4/2)=3.
y3=(y1+y2/2)=(5+7/2)=6.
Therefore P(3,6).
Let the points be(x3,y3).
Given the line segment is perpendicular bisector.
Therefore P is the mid-point of line segment AB.
Using Mid-Point Formula,
x3=(x1+x2/2)=(2+4/2)=3.
y3=(y1+y2/2)=(5+7/2)=6.
Therefore P(3,6).
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The point where the perpendicular bisector of the line segment joining...
Perpendicular Bisector of a Line Segment
The perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to the line segment.
Given Points
The given points are A(2, 5) and B(4, 7).
Midpoint Calculation
To find the midpoint of the line segment joining A and B, we use the midpoint formula:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 4)/2, (5 + 7)/2)
Midpoint = (3, 6)
Equation of Perpendicular Bisector
The slope of the line passing through A and B is (7-5)/(4-2) = 1.
The negative reciprocal of 1 is -1. Therefore, the slope of the perpendicular bisector is -1.
Using the point-slope form of a line, we get:
y - 6 = -1(x - 3)
y - 6 = -x + 3
y = -x + 9
Intersection Point
To find the intersection point of the perpendicular bisector and the line segment, we solve the equations of the two lines simultaneously.
Substitute y = -x + 9 into the equation of the line segment:
-x + 9 = 0
x = 9, then y = 0
Therefore, the point where the perpendicular bisector of the line segment joining A and B cuts is (9, 0), which is not listed as an option.
The perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to the line segment.
Given Points
The given points are A(2, 5) and B(4, 7).
Midpoint Calculation
To find the midpoint of the line segment joining A and B, we use the midpoint formula:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 4)/2, (5 + 7)/2)
Midpoint = (3, 6)
Equation of Perpendicular Bisector
The slope of the line passing through A and B is (7-5)/(4-2) = 1.
The negative reciprocal of 1 is -1. Therefore, the slope of the perpendicular bisector is -1.
Using the point-slope form of a line, we get:
y - 6 = -1(x - 3)
y - 6 = -x + 3
y = -x + 9
Intersection Point
To find the intersection point of the perpendicular bisector and the line segment, we solve the equations of the two lines simultaneously.
Substitute y = -x + 9 into the equation of the line segment:
-x + 9 = 0
x = 9, then y = 0
Therefore, the point where the perpendicular bisector of the line segment joining A and B cuts is (9, 0), which is not listed as an option.
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The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is:a)(6, 3)b)(3, 6)c)(0, 0)d)(2, 5)Correct answer is option 'B'. Can you explain this answer?
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