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Question
A point P (–2, 3) is reflected in line x = 2 to point P’. Find the co-ordinates of P’.
Solution
The image of P (–2, 3) is P' which is reflected in the line x = 2.
The co-ordinates of P' will be (6, 3) as shown in the graph.
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Points (3, 0) and (–1, 0) are invariant points under reflection in the line L1; points (0, –3) and (0, 1) are invariant points on reflection in line L2.
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- State or describe a single transformation that maps P’ onto P''.
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- P is invariant when reflected in an axis. Name the axis.
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(b) Assign special name of quadrilateral AA’B’B.
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Use a graph paper for this question.
(Take 2 cm = 1 unit on both x and y axes)
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- Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.
Points (3, 0) and (-1, 0) are invarient points under reflection in the line L1; point (0, -3) and (0, 1) are invarient points on reflection in line L2.
(i) Write the equation of the line L1 and L2.
(ii) Write down the images of points P(3, 4) and Q(-5, -2) on reflection in L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the image as P'' and Q'' respectively.
