Mathematics
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.
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 90° anticlockwise rotation about the origin transforms a point (x, y) to (-y, x).
The image of the point (5, 6) after a 90° anticlockwise rotation about the origin is (-6, 5).
So, assertion (A) is true.
We know that,
When a point P(x, y) is rotated 90° clockwise about the origin, then the image is (y, -x).
So, reason (R) is true.
∴ Both A and R are correct, and R is not the correct explanation for A.
Hence, option 2 is the correct option.
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Related Questions
The point (-8, 7) is first reflected in x-axis followed by reflection in origin. The resulting point is:
(-8, -7)
(8, 7)
(8, -7)
(-8, 7)
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) : 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.
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.
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.