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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) in the line PP’ Find :
(i) The coordinates of P’ and O’.
(ii) The length of segment PP’ and OO’.
(iii) The perimeter of the quadrilateral POP’O’
(iv) What is the special name of the quadrilateral POP’O’.
Solution
(i) P' (3, -4), O'(6, 0)
(ii) PP'
= `sqrt((3 - 3)^2 + (-4 - 4)^2)`
= `sqrt(64)`
= 8 units
OO'
= `sqrt((0 - 6)^2 + (0 - 0)^2)`
= `sqrt(36)`
= 6 units.
(iii) Perimeter
= 5 + 5 + 5 + 5
= 20 units.
(iv) Rhombus.
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RELATED QUESTIONS
Complete the following table:
| Point | Transformation | Image | |
| (a) | (5, –7) | -------------------- | (–5, 7) |
| (b) | (4, 2) | Reflection in x-axis | ------- |
| (c) | ------- | Reflection in y-axis | (0, 6) |
| (d) | (6, –6) | -------------------- | (–6, 6) |
| (e) | (4, –8) | -------------------- | (–4, –8) |
A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.
State the co-ordinates of the following point under reflection in y-axis:
(6, –3)
S' is the image of S under reflection in the origin. If the co-ordinates of S are (2,-5), write the co-ordinates of S'.
Find the co-ordinates of the image of S(4,-1) after reflection in the line
y = 5
Write down the co-ordinates of the image of (5, – 4).
Reflection in x = 0;
Using a graph paper, plot the points A (6,4) and B (0,4).
(i) Reflect A and B in the origin to get the images A’ and B’.
(ii) Write the co-ordinates of A’ and B’.
(iii) State the geometrical name for. the figure ABA’B’.
(iv) Find its perimeter.
Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axis). P and Q have co-ordinates (0, 5) (- 2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (i).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin following by reflection in x-axis.
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’.
Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axis).
(i) Plot the points A (- 4, 2) and B (2, 4).
(ii) A’ is the image of A when reflected in the y-axis. Plot it on the graph paper and write the coordinates of A’.
(iii) B’ is the image of B when reflected in the line AA’. Write the coordinates of B’.
(iv) Write the geometric name of the figure ABA’B’.
(v) Name a line of symmetry of the figure formed.
