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 :

(i) the co-ordinates of P' and O'.

(ii) the length of the segments PP' and OO',

(iii) the perimeter of the quadrilateral POP'O',

(iv) 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’ = √(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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Similar questions

Q. 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

P P^{^{'}}

. Using Graph paper give :
1) The coordinates of

P^{^{'}}

and

O^{^{'}}

2) The length of segments

P P^{^{'}}

and

O O^{^{'}}

3) The perimeter of the quadrilateral

P O P^{^{'}} O^{^{'}}

4) Geometrical name of the figure

P O P^{^{'}} O^{^{'}}

The point P(3, 4) is reflected to P' in the x axis and O' is the image of O(0, 0) when reflected in the line PP'. Find the perimeter of the quadrilateral POP'O'.

The point P(3, 4) is reflected to P’ in the – axis & O’ is the image of O (the origin) when reflected on line PP’.

(a) Find the perimeter of quadrilateral POP’O’

(b) Name the figure POP’O’

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

(i) Point P (a, b) is reflected in the x-axis to P' (5, -2). Write down the values of a and b.

(ii) P" is the image of P when reflected in the y-axis. Write down the co-ordinates of P".

(iii) Name a single transformation that maps P' to P".

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