Mathematics
The point P(3, 4) is reflected to P' in the x-axis and O' is the image of O(origin) in the line PP'. Find :
(i) the coordinates of P' and O'.
(ii) the length of segments PP' and OO'.
(iii) the perimeter of the quadrilateral POP'O'.
(iv) the geometrical name of the figure POP'O'.
Reflection
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Answer
The graph is shown below:
(i) From graph we get,
The coordinates of P' and O' are (3, -4) and (6, 0) respectively.
(ii) From graph we get,
Length of PP' = 8 units and OO' = 6 units.
(iii) OP = PO' = O'P' = P'O, as all are hypotenuse for same base and perpendicular.
∴ Perimeter of POP'O' is = 4 × OP
The perimeter of the quadrilateral POP'O' is 20 units.
(iv) POP'O' is a rhombus.
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