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The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) is
- a)5x + 2y = 1
- b)4x + 6y = 1
- c)6x + 4y = 1
- d)None
Correct answer is option 'C'. Can you explain this answer?
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Finding the Midpoint
To find the equation of the perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0), we first need to determine the midpoint of the segment.
- Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
- Points: A(1, 2) and B(–2, 0)
Calculating the midpoint:
- M = ((1 + (–2))/2, (2 + 0)/2) = ((–1)/2, 1) = (–0.5, 1)
Finding the Slope
Next, we calculate the slope of the line segment AB.
- Slope formula: m = (y2 - y1) / (x2 - x1)
- Slope of AB = (0 - 2) / (–2 - 1) = (–2) / (–3) = 2/3
Finding the Perpendicular Slope
The slope of the perpendicular bisector is the negative reciprocal of the slope of AB.
- Perpendicular slope = -3/2
Equation of the Perpendicular Bisector
Using the point-slope form of a line equation (y - y1 = m(x - x1)), we substitute the midpoint and the perpendicular slope.
- y - 1 = (-3/2)(x + 0.5)
Rearranging this equation:
- y - 1 = -3/2x - 3/4
- y = -3/2x + 1/4
To express it in standard form, multiply through by 4:
- 4y = -6x + 1
- 6x + 4y = 1
Conclusion
Thus, the equation of the perpendicular bisector is 6x + 4y = 1, which corresponds to option 'C'.
To find the equation of the perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0), we first need to determine the midpoint of the segment.
- Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
- Points: A(1, 2) and B(–2, 0)
Calculating the midpoint:
- M = ((1 + (–2))/2, (2 + 0)/2) = ((–1)/2, 1) = (–0.5, 1)
Finding the Slope
Next, we calculate the slope of the line segment AB.
- Slope formula: m = (y2 - y1) / (x2 - x1)
- Slope of AB = (0 - 2) / (–2 - 1) = (–2) / (–3) = 2/3
Finding the Perpendicular Slope
The slope of the perpendicular bisector is the negative reciprocal of the slope of AB.
- Perpendicular slope = -3/2
Equation of the Perpendicular Bisector
Using the point-slope form of a line equation (y - y1 = m(x - x1)), we substitute the midpoint and the perpendicular slope.
- y - 1 = (-3/2)(x + 0.5)
Rearranging this equation:
- y - 1 = -3/2x - 3/4
- y = -3/2x + 1/4
To express it in standard form, multiply through by 4:
- 4y = -6x + 1
- 6x + 4y = 1
Conclusion
Thus, the equation of the perpendicular bisector is 6x + 4y = 1, which corresponds to option 'C'.
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The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) isa)5x + 2y = 1b)4x + 6y = 1c)6x + 4y = 1d)NoneCorrect answer is option 'C'. Can you explain this answer?
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