Mathematics
Assertion (A): The reflection of the point A(-4, 2) in the origin is the point A'(4, 2).
Reason (R): The image of a point P(x, y) when reflected in the origin is P'(-x, -y).
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Reflection
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Answer
Rule to find reflection of a point in origin :
Change the sign of abscissa i.e. x-coordinate and ordinate i.e. y-coordinate.
A(-4, 2) ⇒ A'(4, -2)
Assertion (A) is false.
Reflection in the origin requires changing the sign of both the x-coordinate and the y-coordinate.
Thus,
P(x, y) ⇒ P'(-x, -y)
Reason (R) is true.
A is false, R is true.
Hence, option 4 is the correct option.
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Related Questions
If the point A(m, n) is first reflected in the y-axis and then reflected in the x-axis to the point A"(-10, 15), then the value of (m - n) is :
-25
-5
5
25
Assertion (A): The point (0, 7) is invariant under the reflection in y-axis.
Reason (R): The image of a point P(x, y) when reflected in the y-axis is P'(x, -y).
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): The point (6, 3) is invariant when reflected in the line x = 6.
Reason (R): A point M(a, y) is invariant on the line x = a.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): The point (-2, 8) is invariant under reflection in line x = -2.
Reason (R): If a point has its x-coordinate 0, it is invariant under refelection in both axes.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.