Mathematics
Assertion (A) : A shape (say circle) can be rotated from one position to another about it centre.
Reason (R) : Rotation is defined by (i)the angle of rotation, (ii) the direction of rotation and the centre of rotation.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Symmetry
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Answer
A circle can be rotated about its center by any angle, and it will still look exactly the same because all points on the circle are equidistant from the center.
So, assertion (A) is true.
Angle of Rotation determines the amount of turning involved in the rotation.
Direction of Rotation indicates whether the rotation is clockwise or counterclockwise.
Center of Rotation is the fixed point around which the object rotates.
Thus, rotation is defined by (i)the angle of rotation, (ii) the direction of rotation and the centre of rotation.
So, reason (R) is true.
∴ Both A and R are correct, and R is the correct explanation for A.
Hence, option 1 is the correct option.
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Related Questions
Statement 1: A point P is reflected to P' in a line L, then the line L is the right bisector of PP'.
Statement 2: A point P is reflected to P' in a line L, then the line PP' is the right bisector of L.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A) : The image of a point A(5, 6) under an anticlockwise rotation of 90°, about the origin is A'(-6, 5).
Reason (R) : When a point P is rotated through 90° clockwise direction about the origin, then abscissa of the given point becomes the ordinate with opposite sign of the resultant point and the ordinate of the given point becomes the abscissa of the resultant point.
Both A and R are correct, and R is the correct explanation for A.
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A is true, but R is false.
A is false, but R is true.
Assertion (A) : An equilateral triangle has a point of symmetry.
Reason (R) : A plane figure is said to have a point symmetry about a point, if every line segment drawn in the given figure passing through it is bisected by this point.
Both A and R are correct, and R is the correct explanation for A.
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A is true, but R is false.
A is false, but R is true.
Assertion (A) : A parallelogram has a rotational symmetry of order 2 about the point of intersection O of its diagonals.
Reason (R) : A plane figure is said to have rotational symmetry if it aligns with the original position only once while being rotated about 360°.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are incorrect.
A is true, but R is false.
A is false, but R is true.