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If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.?
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If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and t...
Given Information:
- Two adjacent vertices of a parallelogram are (3,2) and (-1,0).
- The diagonals intersect at (2, -5).
Finding the Coordinates of the Other Two Vertices:
1. Midpoint Formula:
To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we use the formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
2. Midpoint of Diagonal:
Given that the diagonals of a parallelogram intersect at (2, -5), we can find the midpoint of the diagonal formed by (3,2) and (-1,0) using the midpoint formula:
Midpoint of diagonal AC = ((3 + (-1)) / 2, (2 + 0) / 2)
Midpoint of diagonal AC = (1, 1)
3. Find the Other Two Vertices:
Since the diagonals of a parallelogram bisect each other, the midpoint of the diagonals is the center of the parallelogram.
Let the other two vertices of the parallelogram be B and D.
- The midpoint of BD = Midpoint of AC = (1, 1)
- Given that the diagonals intersect at (2, -5), the midpoint of the other diagonal BD is also (1, 1).
4. Using Midpoint Formula:
Let the coordinates of B be (x, y).
Using the midpoint formula for the line segment with endpoints (3,2) and (x, y) as (1, 1), we get:
Midpoint = ((3 + x) / 2, (2 + y) / 2) = (1, 1)
Solving these equations, we get x = -1 and y = 1.
5. Final Coordinates of the Other Two Vertices:
Therefore, the coordinates of the other two vertices are (-1, 1) and (5, -3).
- Two adjacent vertices of a parallelogram are (3,2) and (-1,0).
- The diagonals intersect at (2, -5).
Finding the Coordinates of the Other Two Vertices:
1. Midpoint Formula:
To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we use the formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
2. Midpoint of Diagonal:
Given that the diagonals of a parallelogram intersect at (2, -5), we can find the midpoint of the diagonal formed by (3,2) and (-1,0) using the midpoint formula:
Midpoint of diagonal AC = ((3 + (-1)) / 2, (2 + 0) / 2)
Midpoint of diagonal AC = (1, 1)
3. Find the Other Two Vertices:
Since the diagonals of a parallelogram bisect each other, the midpoint of the diagonals is the center of the parallelogram.
Let the other two vertices of the parallelogram be B and D.
- The midpoint of BD = Midpoint of AC = (1, 1)
- Given that the diagonals intersect at (2, -5), the midpoint of the other diagonal BD is also (1, 1).
4. Using Midpoint Formula:
Let the coordinates of B be (x, y).
Using the midpoint formula for the line segment with endpoints (3,2) and (x, y) as (1, 1), we get:
Midpoint = ((3 + x) / 2, (2 + y) / 2) = (1, 1)
Solving these equations, we get x = -1 and y = 1.
5. Final Coordinates of the Other Two Vertices:
Therefore, the coordinates of the other two vertices are (-1, 1) and (5, -3).
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If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.?
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If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.?.
If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.?.
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