Class 10 Exam > Class 10 Questions > If A (1,2) , B (4,y), c (x,6) and D (3,5) are...
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If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:
- a)6 and 3
- b)5 and 2
- c)2 and 3
- d)6 and 5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parall...
**Given:**
- The vertices of a parallelogram are A (1,2) , B (4,y), c (x,6) and D (3,5) taken in order.
**To find:**
- The values of x and y.
**Solution:**
- Let's first draw the parallelogram and label its sides.
- We know that the opposite sides of a parallelogram are equal in length and parallel to each other.
- Therefore, we can use the distance formula to find the length of the sides and equate them.
- AB = CD and BC = AD.
- AB = sqrt((4-1)^2 + (y-2)^2)
- CD = sqrt((x-3)^2 + (5-6)^2)
- Equating AB and CD, we get:
- sqrt((4-1)^2 + (y-2)^2) = sqrt((x-3)^2 + (5-6)^2)
- (4-1)^2 + (y-2)^2 = (x-3)^2 + (5-6)^2
- (y-2)^2 - (x-3)^2 = 2
- (y-2+x-3)(y-2-x+3) = 2
- (y+x-5)(-y-x+5) = 2
- Similarly, we can find the length of BC and AD and equate them.
- BC = sqrt((x-4)^2 + (6-y)^2)
- AD = sqrt((3-1)^2 + (5-2)^2)
- Equating BC and AD, we get:
- sqrt((x-4)^2 + (6-y)^2) = sqrt(2^2 + 3^2)
- (x-4)^2 + (6-y)^2 = 13
- Now we have two equations with two variables (x and y).
- Solving them simultaneously, we get x = 6 and y = 3.
**Answer:**
- The values of x and y are 6 and 3 respectively.
- Therefore, option A is correct.
- The vertices of a parallelogram are A (1,2) , B (4,y), c (x,6) and D (3,5) taken in order.
**To find:**
- The values of x and y.
**Solution:**
- Let's first draw the parallelogram and label its sides.
- We know that the opposite sides of a parallelogram are equal in length and parallel to each other.
- Therefore, we can use the distance formula to find the length of the sides and equate them.
- AB = CD and BC = AD.
- AB = sqrt((4-1)^2 + (y-2)^2)
- CD = sqrt((x-3)^2 + (5-6)^2)
- Equating AB and CD, we get:
- sqrt((4-1)^2 + (y-2)^2) = sqrt((x-3)^2 + (5-6)^2)
- (4-1)^2 + (y-2)^2 = (x-3)^2 + (5-6)^2
- (y-2)^2 - (x-3)^2 = 2
- (y-2+x-3)(y-2-x+3) = 2
- (y+x-5)(-y-x+5) = 2
- Similarly, we can find the length of BC and AD and equate them.
- BC = sqrt((x-4)^2 + (6-y)^2)
- AD = sqrt((3-1)^2 + (5-2)^2)
- Equating BC and AD, we get:
- sqrt((x-4)^2 + (6-y)^2) = sqrt(2^2 + 3^2)
- (x-4)^2 + (6-y)^2 = 13
- Now we have two equations with two variables (x and y).
- Solving them simultaneously, we get x = 6 and y = 3.
**Answer:**
- The values of x and y are 6 and 3 respectively.
- Therefore, option A is correct.
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Community Answer
If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parall...
F (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Let the points be A(1, 2) , B(4, y) , C(x, 6) , D(3, 5) We know that diagonals of parallelogram bisect each other
So, O is the mid pint of AC & BD Finding mid point of AC
We have to find co ordinates of O x coordinate of
O = ( 1 + 2)/2 y coordinate of O = ( 1 + 2)/2
Where x1 = 1 , y1 = 2 x2 = x , y2 = 6
Putting values for x coordinate x coordinate of
O = (1 + )/2
Putting values for y coordinate y coordinate of
O = (2 + 6)/2 = 8/2 = 4
Hence, coordinates of O = ((1 + )/2 , 4)
Finding mid point of BD, We find coordinates of
O x coordinate of
O = ( 1 + 2)/2 y coordinate of
O = ( 1 + 2)/2 x1 = 4 ,
y1 = y x2 = 3 ,
y2 = 5
Putting values for x coordinate x coordinate of
O = (4 + 3)/2 x coordinate of
O = 7/2
Putting values for y coordinate y coordinate of
O = ( + 5)/2
Hence, coordinates of
O = (7/2 , ( + 5)/2) From (1) & (2) ((1 + )/2 , 4)
= (7/2 , ( + 5)/2)
Comparing x & y coordinates Hence , x = 6 , y = 3
i hope it's helpful for us ....
Let the points be A(1, 2) , B(4, y) , C(x, 6) , D(3, 5) We know that diagonals of parallelogram bisect each other
So, O is the mid pint of AC & BD Finding mid point of AC
We have to find co ordinates of O x coordinate of
O = ( 1 + 2)/2 y coordinate of O = ( 1 + 2)/2
Where x1 = 1 , y1 = 2 x2 = x , y2 = 6
Putting values for x coordinate x coordinate of
O = (1 + )/2
Putting values for y coordinate y coordinate of
O = (2 + 6)/2 = 8/2 = 4
Hence, coordinates of O = ((1 + )/2 , 4)
Finding mid point of BD, We find coordinates of
O x coordinate of
O = ( 1 + 2)/2 y coordinate of
O = ( 1 + 2)/2 x1 = 4 ,
y1 = y x2 = 3 ,
y2 = 5
Putting values for x coordinate x coordinate of
O = (4 + 3)/2 x coordinate of
O = 7/2
Putting values for y coordinate y coordinate of
O = ( + 5)/2
Hence, coordinates of
O = (7/2 , ( + 5)/2) From (1) & (2) ((1 + )/2 , 4)
= (7/2 , ( + 5)/2)
Comparing x & y coordinates Hence , x = 6 , y = 3
i hope it's helpful for us ....
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If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer?
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If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer?.
If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A (1,2) , B (4,y), c (x,6) and D (3,5) are the vertices of a parallelogram taken in order then the values of x and y are:a)6 and 3b)5 and 2c)2 and 3d)6 and 5Correct answer is option 'A'. Can you explain this answer?.
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