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Question
The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’. Write:
- the co-ordinates of P’ and O’.
- the length of the segments PP’ and OO’.
- the perimeter of the quadrilateral POP’O’.
- the geometrical name of the figure POP’O’.
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Solution
i. Co-ordinates of P’ and O’ are (3, –4) and (6, 0) respectively.
ii. PP’ = 8 units and OO’ = 6 units.
iii. From the graph it is clear that all sides of the quadrilateral POP’O’ are equal.
In right Δ PO’Q, PO’ = `sqrt((4)^2 + (3)^2)` = 5 units
So, perimeter of quadrilateral POP’O’ = 4 PO’ = 4 × 5 units = 20 units
iv. Quadrilateral POP’O’ is a rhombus.
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