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Question
- Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
- 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.
- 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.
- Write down the geometrical name of the figure AA’BB’.
- Name the invariant points under reflection in the x-axis.
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Solution
- The points A (3, 5) and B (–2, –4) can be plotted on a graph as shown.
- A’ = Image of A when reflected in the x-axis = (3, –5)
- C = Image of B when reflected in the y-axis = (2, –4) B’ = Image when C is reflected in the origin = (–2, 4)
- Isosceles trapezium
- Any point that remains unaltered under a given transformation is called an invariant. Thus, the required two points are (3, 0) and (–2, 0).
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- B” of B under reflection in the line AA”.
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- the length of the segments PP’ and OO’.
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P and Q have co-ordinates (0, 5) and (–2, 4).
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- (0, k) on reflection in the origin is invariant. Write the value of k.
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The triangle ABC, where A is (2, 6), B is (–3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C".
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Using a graph paper, plot the point A (6, 4) and B (0, 4).
(a) Reflect A and B in the origin to get the image A’ and B’.
(b) Write the co-ordinates of A’ and B’.
(c) Sate the geometrical name for the figure ABA’B’.
(d) Find its perimeter.
Use graph paper for this question.
(Take 2 cm = 1 unit along both x-axis and y-axis.)
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- Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
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- State the line of symmetry of this figure.
Use a graph paper for this question.
(Take 2 cm = 1 unit on both x and y axes)
- Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
- Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
- 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.
