Quantitative Aptitude
GEOMETRY MCQs
Coordinate Geometry, Coordinate Geometry (10th Grade), Three Dimensional Geometry (10th Grade)
Total Questions : 133
| Page 2 of 14 pages
Answer: Option C. -> 5units
Answer: Option B. -> 4ax
Answer: Option A. -> 3, 0
Answer: Option B. -> 4, 0
Answer: Option A. -> isosceles
Answer: Option B. -> an isosceles right angled triangle
Answer: Option C. -> a square
Answer: Option A. -> a rectangle
Answer: Option D. -> parallelogram
A parallelogram is a quadrilateral which has two pairs of parallel sides. It can be defined as a four sided shape which has opposite sides that are both equal in length and parallel to each other.
We will now check if the given quadrilateral ABCD is a parallelogram.
• The coordinates of the vertices of the quadrilateral ABCD are A(0, 0), B(4, 4), C(4, 8) and D(0, 4).
• The length of the sides can be calculated using the distance formula.
• The distance between A and B is √((4-0)2 + (4-0)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between B and C is √((4-4)2 + (8-4)2) = √(02+42) = √(0+16) = 4
• The distance between C and D is √((4-0)2 + (8-4)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between D and A is √((0-0)2 + (4-0)2) = √(02+42) = √(0+16) = 4
From the above calculations, we can see that the lengths of the opposite sides of the quadrilateral ABCD are same, i.e. AB = CD and AD = BC. Therefore, the quadrilateral ABCD is a parallelogram.
A parallelogram is a quadrilateral which has two pairs of parallel sides. It can be defined as a four sided shape which has opposite sides that are both equal in length and parallel to each other.
We will now check if the given quadrilateral ABCD is a parallelogram.
• The coordinates of the vertices of the quadrilateral ABCD are A(0, 0), B(4, 4), C(4, 8) and D(0, 4).
• The length of the sides can be calculated using the distance formula.
• The distance between A and B is √((4-0)2 + (4-0)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between B and C is √((4-4)2 + (8-4)2) = √(02+42) = √(0+16) = 4
• The distance between C and D is √((4-0)2 + (8-4)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between D and A is √((0-0)2 + (4-0)2) = √(02+42) = √(0+16) = 4
From the above calculations, we can see that the lengths of the opposite sides of the quadrilateral ABCD are same, i.e. AB = CD and AD = BC. Therefore, the quadrilateral ABCD is a parallelogram.
Answer: Option D. -> none of these
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