Mathematics
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.
Reflection
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Answer
Reflection in the line x = -2 means the mirror line passes through x = -2. Any point lying on that line will remain unchanged after reflection.
Therefore, after reflection the point remains (-2, 8).
Assertion (A) is True.
Let us consider a point (0, y):
On reflection in y-axis, the sign of x-coordinate changes,
(0, y) ⇒ (0, y)
On reflection in x-axis, the sign of y-coordinate changes,
(0, y) ⇒ (0, -y).
So it is not invariant under both axes.
Reason (R) is false.
A is true, R is false.
Hence, option 3 is the correct option.
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Related Questions
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).
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ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.
(a) Point P(2, -3) on reflection becomes P'(2, 3). Name the line of reflection (say L1).
(b) Point P' is reflected to P'' along the line (𝐿2), which is perpendicular to the line 𝐿1 and passes through the point, which is invariant along both axes. Write the coordinates of P''.
(c) Name and write the coordinates of the point of intersection of the lines 𝐿1 and 𝐿2.
(d) Point P is reflected to P''' on reflection through the point named in the answer of part I of this question. Write the coordinates of P'''. Comment on the location of the points P'' and P'''.