Mathematics
The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".
(i) Write down the co-ordinates of A".
(ii) Write down a single transformation that maps A onto A".
Reflection
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Answer
(i) Reflection in x-axis is given by,
Mx(x, y) = (x, -y)
∴ Image on reflection of A(-3, 2) in x-axis = A'(-3, -2)
Reflection in origin is given by,
Mo(x, y) = (-x, -y)
∴ Image on reflection of A'(-3, -2) in origin = A"(3, 2)
Hence, co-ordinates of A" = (3, 2).
(ii) Transformation from A to A" is,
A(-3, 2) = A"(3, 2).
Reflection in y-axis is given by,
My(x, y) = (-x, y)
∴ Image on reflection of A(-3, 2) in y-axis = A''(3, 2)
Hence, the single transformation that maps A onto A" is reflection in y-axis.
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Related Questions
A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).
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(ii) Find the co-ordinates of the image of P under reflection in the x-axis.
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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".
(i) Write down the co-ordinates of A", B" and C".
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Attempt this question on graph paper.
(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
(b) Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper.
(c) Write down :
(i) the geometrical name of the figure ABB'A';
(ii) the measure of angle ABB';
(iii) the image A" of A, when A is reflected in the origin.
(iv) the single transformation that maps A' to A".