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Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are
- a)(−3, 4)
- b)(0, 11)
- c)(4, 5)
- d)(−4, 5)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let ABCD be a parallelogram such that the coordinates of its three ver...
In a parallelogram, two diagonals of parallelogram bisects each other, which concludes that mid-point of both diagonals are the same.
x = -4 and y = 5
The answer is option D.
Most Upvoted Answer
Let ABCD be a parallelogram such that the coordinates of its three ver...
Let's call the fourth vertex D.
Since ABCD is a parallelogram, the opposite sides are parallel and equal in length. Therefore, the vector representing AB is equal to the vector representing DC.
The vector representing AB is (3-1, 4-1) = (2, 3).
So, the coordinates of D can be found by adding the vector (2, 3) to the coordinates of C.
C = (x, y)
D = (x + 2, y + 3)
Since ABCD is a parallelogram, the opposite sides are also parallel and equal in length. Therefore, the vector representing BC is equal to the vector representing AD.
The vector representing BC is (x + 2 - 3, y + 3 - 4) = (x - 1, y - 1).
So, the coordinates of D can be found by subtracting the vector (x - 1, y - 1) from the coordinates of B.
B = (3, 4)
D = (3 - (x - 1), 4 - (y - 1))
= (4 - x, 5 - y)
Since D has the same coordinates whether it is obtained by adding the vector (2, 3) to C or subtracting the vector (x - 1, y - 1) from B, we can equate the coordinates of D.
x + 2 = 4 - x
2x = 2
x = 1
y + 3 = 5 - y
2y = 2
y = 1
Therefore, the coordinates of D are (1 + 2, 1 + 3) = (3, 4).
So, the coordinates of the fourth vertex D are (3, 4).
Since ABCD is a parallelogram, the opposite sides are parallel and equal in length. Therefore, the vector representing AB is equal to the vector representing DC.
The vector representing AB is (3-1, 4-1) = (2, 3).
So, the coordinates of D can be found by adding the vector (2, 3) to the coordinates of C.
C = (x, y)
D = (x + 2, y + 3)
Since ABCD is a parallelogram, the opposite sides are also parallel and equal in length. Therefore, the vector representing BC is equal to the vector representing AD.
The vector representing BC is (x + 2 - 3, y + 3 - 4) = (x - 1, y - 1).
So, the coordinates of D can be found by subtracting the vector (x - 1, y - 1) from the coordinates of B.
B = (3, 4)
D = (3 - (x - 1), 4 - (y - 1))
= (4 - x, 5 - y)
Since D has the same coordinates whether it is obtained by adding the vector (2, 3) to C or subtracting the vector (x - 1, y - 1) from B, we can equate the coordinates of D.
x + 2 = 4 - x
2x = 2
x = 1
y + 3 = 5 - y
2y = 2
y = 1
Therefore, the coordinates of D are (1 + 2, 1 + 3) = (3, 4).
So, the coordinates of the fourth vertex D are (3, 4).
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Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer?
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Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer?.
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Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D area)(−3, 4)b)(0, 11)c)(4, 5)d)(−4, 5)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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