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Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the sum of all possible xco ordinates of the fourth vertex of the parallelogram is
- a)11
- b)8
- c)7
- d)6
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the s...
Given:
Three vertices of a parallelogram are (1, 2), (3, 8), and (4, 1).
To find:
The sum of all possible x-coordinates of the fourth vertex of the parallelogram.
Solution:
Step 1: Determine the fourth vertex
Since opposite sides of a parallelogram are parallel, the fourth vertex can be found by translating one of the given vertices to the opposite side.
Let's take the first given vertex (1, 2) and translate it to the opposite side, which is the line passing through (3, 8) and (4, 1). The translation vector can be found by subtracting the coordinates of the first given vertex from the coordinates of the second given vertex:
Translation vector = (3, 8) - (1, 2) = (2, 6)
Now, add this translation vector to the coordinates of the first given vertex to find the fourth vertex:
Fourth vertex = (1, 2) + (2, 6) = (3, 8)
So, the fourth vertex is (3, 8).
Step 2: Find the sum of all possible x-coordinates
The x-coordinate of the fourth vertex is 3.
There is only one possible x-coordinate for the fourth vertex, which is 3.
Therefore, the sum of all possible x-coordinates of the fourth vertex is 3.
Answer:
Option B) 8
Three vertices of a parallelogram are (1, 2), (3, 8), and (4, 1).
To find:
The sum of all possible x-coordinates of the fourth vertex of the parallelogram.
Solution:
Step 1: Determine the fourth vertex
Since opposite sides of a parallelogram are parallel, the fourth vertex can be found by translating one of the given vertices to the opposite side.
Let's take the first given vertex (1, 2) and translate it to the opposite side, which is the line passing through (3, 8) and (4, 1). The translation vector can be found by subtracting the coordinates of the first given vertex from the coordinates of the second given vertex:
Translation vector = (3, 8) - (1, 2) = (2, 6)
Now, add this translation vector to the coordinates of the first given vertex to find the fourth vertex:
Fourth vertex = (1, 2) + (2, 6) = (3, 8)
So, the fourth vertex is (3, 8).
Step 2: Find the sum of all possible x-coordinates
The x-coordinate of the fourth vertex is 3.
There is only one possible x-coordinate for the fourth vertex, which is 3.
Therefore, the sum of all possible x-coordinates of the fourth vertex is 3.
Answer:
Option B) 8
Community Answer
Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the s...
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Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the sum of all possible xco ordinates of the fourth vertex of the parallelogram isa)11b)8c)7d)6Correct answer is option 'B'. Can you explain this answer?
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Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the sum of all possible xco ordinates of the fourth vertex of the parallelogram isa)11b)8c)7d)6Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the sum of all possible xco ordinates of the fourth vertex of the parallelogram isa)11b)8c)7d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (1, 2), (3, 8), (4, 1) are three vertices of a parallelogram the sum of all possible xco ordinates of the fourth vertex of the parallelogram isa)11b)8c)7d)6Correct answer is option 'B'. Can you explain this answer?.
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