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If a, b, c and d are the position vectors of the points A, B, C and D such that a + c = b + d, then ABCD is a
- a)Trapezium
- b)Rectangle
- c)Square
- d)Parallelogram
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If a, b, c and d are the position vectors of the points A, B, C and D ...
Given:
If we divide both sides with 2 we get,
If we divide both sides with 2 we get,
⇒ Mid pt. of AC = Mid. pt. of BD
∴ ABCD is a parallelogram.
∴ ABCD is a parallelogram.
Most Upvoted Answer
If a, b, c and d are the position vectors of the points A, B, C and D ...
Given, a, b, c, and d are position vectors of points A, B, C, and D respectively.
We know that the position vector of a point is the vector that starts from the origin and ends at that point.
a c = b d implies that the vectors a – c and b – d are parallel.
This means that the line passing through A and C is parallel to the line passing through B and D.
Hence, we can conclude that ABCD is a parallelogram.
Now, let's see why ABCD cannot be a rectangle, square or trapezium.
Why ABCD cannot be a rectangle?
A rectangle has four right angles. However, we don't know anything about the angles of ABCD. Hence, we cannot conclude that ABCD is a rectangle.
Why ABCD cannot be a square?
A square is a special type of rectangle that has all sides equal. We don't know anything about the sides of ABCD. Hence, we cannot conclude that ABCD is a square.
Why ABCD cannot be a trapezium?
A trapezium is a quadrilateral that has at least one pair of parallel sides. ABCD is a parallelogram and hence has two pairs of parallel sides. Therefore, ABCD cannot be a trapezium.
Hence, the correct answer is option 'D' - ABCD is a parallelogram.
We know that the position vector of a point is the vector that starts from the origin and ends at that point.
a c = b d implies that the vectors a – c and b – d are parallel.
This means that the line passing through A and C is parallel to the line passing through B and D.
Hence, we can conclude that ABCD is a parallelogram.
Now, let's see why ABCD cannot be a rectangle, square or trapezium.
Why ABCD cannot be a rectangle?
A rectangle has four right angles. However, we don't know anything about the angles of ABCD. Hence, we cannot conclude that ABCD is a rectangle.
Why ABCD cannot be a square?
A square is a special type of rectangle that has all sides equal. We don't know anything about the sides of ABCD. Hence, we cannot conclude that ABCD is a square.
Why ABCD cannot be a trapezium?
A trapezium is a quadrilateral that has at least one pair of parallel sides. ABCD is a parallelogram and hence has two pairs of parallel sides. Therefore, ABCD cannot be a trapezium.
Hence, the correct answer is option 'D' - ABCD is a parallelogram.
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Community Answer
If a, b, c and d are the position vectors of the points A, B, C and D ...
In parallelogram, if u see algebraically, diagonals are of equal length and thus , magnitude of vector is equal in this question as given. actually it is always equal. further , if u have any more doubt on this , refer parallelogram law of vector addition.
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If a, b, c and d are the position vectors of the points A, B, C and D such that a + c = b + d, then ABCD is aa)Trapeziumb)Rectanglec)Squared)ParallelogramCorrect answer is option 'D'. Can you explain this answer?
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