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The points which lies on the perpendicular bisector of the line segment joining the points A (-2, -5), B (2, 5) is
- a)(0, 0)
- b)(0, 2)
- c)(2 , 0)
- d)(- 2 , 0)
Correct answer is option 'A'. Can you explain this answer?
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Solution:
Finding the midpoint of AB
First, we need to find the midpoint of line segment AB.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) = (-2, -5) and (x2, y2) = (2, 5)
Midpoint = ((-2 + 2)/2, (-5 + 5)/2)
Midpoint = (0, 0)
Finding the equation of the line perpendicular to AB
The line perpendicular to AB will have a slope that is negative reciprocal of the slope of AB.
Slope of AB = (change in y)/(change in x) = (5 - (-5))/(2 - (-2)) = 10/4 = 5/2
Negative reciprocal slope = -2/5
Using point-slope form of equation
y - y1 = m(x - x1)
Where (x1, y1) = (0, 0) and m = -2/5
y - 0 = (-2/5)(x - 0)
y = (-2/5)x
The equation of the perpendicular bisector of AB is y = (-2/5)x.
Finding the points on the perpendicular bisector
To find the points on the perpendicular bisector, we substitute different values of x into the equation y = (-2/5)x and solve for y.
For x = 0, y = 0
For x = 5, y = (-2/5)(5) = -2
For x = -5, y = (-2/5)(-5) = 2
Therefore, the points on the perpendicular bisector are (0, 0), (5, -2), and (-5, 2).
Conclusion:
The correct answer is option 'A' (0, 0). The points which lie on the perpendicular bisector of AB are (0, 0), (5, -2), and (-5, 2), but only (0, 0) is one of the options given.
Finding the midpoint of AB
First, we need to find the midpoint of line segment AB.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) = (-2, -5) and (x2, y2) = (2, 5)
Midpoint = ((-2 + 2)/2, (-5 + 5)/2)
Midpoint = (0, 0)
Finding the equation of the line perpendicular to AB
The line perpendicular to AB will have a slope that is negative reciprocal of the slope of AB.
Slope of AB = (change in y)/(change in x) = (5 - (-5))/(2 - (-2)) = 10/4 = 5/2
Negative reciprocal slope = -2/5
Using point-slope form of equation
y - y1 = m(x - x1)
Where (x1, y1) = (0, 0) and m = -2/5
y - 0 = (-2/5)(x - 0)
y = (-2/5)x
The equation of the perpendicular bisector of AB is y = (-2/5)x.
Finding the points on the perpendicular bisector
To find the points on the perpendicular bisector, we substitute different values of x into the equation y = (-2/5)x and solve for y.
For x = 0, y = 0
For x = 5, y = (-2/5)(5) = -2
For x = -5, y = (-2/5)(-5) = 2
Therefore, the points on the perpendicular bisector are (0, 0), (5, -2), and (-5, 2).
Conclusion:
The correct answer is option 'A' (0, 0). The points which lie on the perpendicular bisector of AB are (0, 0), (5, -2), and (-5, 2), but only (0, 0) is one of the options given.
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The points which lies on the perpendicular bisector of the line segment joining the points A (-2, -5), B (2, 5) isa)(0, 0)b)(0, 2)c)(2 , 0)d)(- 2 , 0)Correct answer is option 'A'. Can you explain this answer?
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