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Question
A point P(a, b) is reflected in the X-axis to P'(2, – 3). Write down the value of a & b. P” is the image of P, when reflected on the Y-axis. Write down the co-ordinates of P” when P is reflected in the line parallel to the Y-axis, such that x = 4.
Solution
Reflection of P (a, b) on the X-axis P' (a, -b)
(i) ∴ P' (a, -b) = P' (2, -3)
+ a = + 2, ∴ a = 2
-b = -3, ∴ b = 3
P (2, 3)
(ii) P'' is the image of P(2, 3) under reflection Y-axis = P''(-2, 3).
(iii) P''' is the image of P(2, 3) under reflection x = 4
⇒ P'''(6, 3).
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RELATED QUESTIONS
State the co-ordinates of the following point under reflection in y-axis:
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A point P (-8, 1) is reflected in the x-axis to the point P'. The point P' is then reflected in the origin to point P". Write down the co-ordinates of P". State the single transformation that maps P into P".
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Reflection in x = 0;
A point P(4, – 1) is reflected to P’ in the line y = 2 followed by the reflection to P” in the line x = -1. Find :
(i) The co-ordinates of P’.
(ii) The co-ordinates of P”.
(iii) The length of PP’.
(iv) The length of P’P”.
Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axis):
(i) Plot A (4, 4), B (4, – 6) and C (8, 0), the vertices of a triangle ABC.
(ii) Reflect ABC on the y-axis and name it as A’B’C’.
(iii) Write the coordinates of the images A’, B’ and C’.
(iv) Give a geometrical name for the figure AA’ C’B’ BC.
(v) Identify the line of symmetry of AA’ C’ B’ BC.
Use graph paper to answer this question:
(i) Plot the points A (4,6) and B (1, 2).
(ii) A’ is the image of A when reflected in X-axis,
(iii) B’ is the image of B when B is reflected in the line AA’.
(iv) Give the geometrical name for the figure ABA’B’.
