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If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?
- a)y = 1/2x+b
- b)y = -1/2x+b
- c)y = 2x+3/2
- d)y = -1/2x+1/2
- e)y = 3/2x - 1/2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the coordinates of point A are (2,2) and the coordinates of point B...
Step 1: Find the midpoint of AB The midpoint of AB can be found by taking the average of the x-coordinates and the average of the y-coordinates:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 0)/2, (2 + (-2))/2)
Midpoint = (1, 0)
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 0)/2, (2 + (-2))/2)
Midpoint = (1, 0)
Step 2: Determine the slope of AB The slope of AB can be calculated using the formula:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 - 2)/(0 - 2)
Slope (m) = (-4)/(-2)
Slope (m) = 2
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 - 2)/(0 - 2)
Slope (m) = (-4)/(-2)
Slope (m) = 2
Step 3: Find the negative reciprocal of the slope from step 2
The negative reciprocal of 2 is -1/2.
The negative reciprocal of 2 is -1/2.
Step 4: Use the midpoint and the negative reciprocal slope to form the equation in slope-intercept form
Using the midpoint (1, 0) and the negative reciprocal slope of -1/2, the equation of the perpendicular bisector is:
y = (-1/2)x + b
Using the midpoint (1, 0) and the negative reciprocal slope of -1/2, the equation of the perpendicular bisector is:
y = (-1/2)x + b
To find the value of b, substitute the coordinates of the midpoint (1, 0):
0 = (-1/2)(1) + b
0 = -1/2 + b
b = 1/2
0 = (-1/2)(1) + b
0 = -1/2 + b
b = 1/2
Therefore, the equation of the perpendicular bisector is:
y = -1/2x + 1/2
y = -1/2x + 1/2
The correct answer is D.
Community Answer
If the coordinates of point A are (2,2) and the coordinates of point B...
Step 1: Find the midpoint of AB The midpoint of AB can be found by taking the average of the x-coordinates and the average of the y-coordinates:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 0)/2, (2 + (-2))/2)
Midpoint = (1, 0)
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint = ((2 + 0)/2, (2 + (-2))/2)
Midpoint = (1, 0)
Step 2: Determine the slope of AB The slope of AB can be calculated using the formula:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 - 2)/(0 - 2)
Slope (m) = (-4)/(-2)
Slope (m) = 2
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 - 2)/(0 - 2)
Slope (m) = (-4)/(-2)
Slope (m) = 2
Step 3: Find the negative reciprocal of the slope from step 2
The negative reciprocal of 2 is -1/2.
The negative reciprocal of 2 is -1/2.
Step 4: Use the midpoint and the negative reciprocal slope to form the equation in slope-intercept form
Using the midpoint (1, 0) and the negative reciprocal slope of -1/2, the equation of the perpendicular bisector is:
y = (-1/2)x + b
Using the midpoint (1, 0) and the negative reciprocal slope of -1/2, the equation of the perpendicular bisector is:
y = (-1/2)x + b
To find the value of b, substitute the coordinates of the midpoint (1, 0):
0 = (-1/2)(1) + b
0 = -1/2 + b
b = 1/2
0 = (-1/2)(1) + b
0 = -1/2 + b
b = 1/2
Therefore, the equation of the perpendicular bisector is:
y = -1/2x + 1/2
y = -1/2x + 1/2
The correct answer is D.
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If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?a)y = 1/2x+bb)y = -1/2x+bc)y = 2x+3/2d)y = -1/2x+1/2e)y = 3/2x - 1/2Correct answer is option 'D'. Can you explain this answer?
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If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?a)y = 1/2x+bb)y = -1/2x+bc)y = 2x+3/2d)y = -1/2x+1/2e)y = 3/2x - 1/2Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?a)y = 1/2x+bb)y = -1/2x+bc)y = 2x+3/2d)y = -1/2x+1/2e)y = 3/2x - 1/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?a)y = 1/2x+bb)y = -1/2x+bc)y = 2x+3/2d)y = -1/2x+1/2e)y = 3/2x - 1/2Correct answer is option 'D'. Can you explain this answer?.
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