Question
Download Solution PDFConsider a parallelogram whose vertices are A (1, 2), B (4, y), C (x, 6) and D (3, 5) taken in order
What is the point of intersection of the diagonals?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and the opposite angles are equal in measure.
- Diagonals of parallelogram bisect each other.
- Midpoint formula:
Suppose x, y are midpoints then)
Where,
Calculation:
Here, A (1, 2), B (4, y), C (x, 6) and D (3, 5) are the vertices of parallelogram.
AB = CD and AD = BC (sides of parallelogram)
AC and BD are the diagonals which bisect each other.
Suppose diagonals intersect each other at (m, n)
Midpoint of AC =
Midpoint of BD =
We can see that,
Midpoint of AC = midpoint of BD
The point of intersection of diagonals = Midpoint of AC
(m, n) =
=
=
Hence, option 1 is correct.
Additional point:
- Suppose p & q are length of diagonals and a & b are length of sides of parallelogram then we have relation
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