Mathematics
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".
(ii) Write down a single transformation that maps triangle ABC onto triangle A"B"C".
Reflection
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Answer
(i) On reflection of point A in y-axis,
A(2, 6) = A'(-2, 6)
On reflection of point A' in origin,
A'(-2, 6) = A"(2, -6).
On reflection of point B in y-axis,
B(-3, 5) = B'(3, 5)
On reflection of point B' in origin,
B'(3, 5) = B"(-3, -5).
On reflection of point C in y-axis,
C(4, 7) = C'(-4, 7)
On reflection of point C' in origin,
C'(-4, 7) = C"(4, -7).
Hence, co-ordinates of A" = (2, -6), B" = (-3, -5), C" = (4, -7).
(ii) Transformation,
A(2, 6) = A"(2, -6), B(-3, 5) = B"(-3, -5) and C(4, 7) = C"(4, -7)
The single transformation that maps above transformation is reflection in x-axis.
Hence, reflection in x-axis maps triangle ABC onto triangle A"B"C".
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Related Questions
The point P(a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P' has co-ordinates (4, 6); evaluate a and b.
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".
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".
Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1; points (0, -3) and (0, 1) are invariant points on reflection in line L2.
(i) Name and write equations for the lines L1 and L2.
(ii) Write down the images of points P(3, 4) and Q(-5, -2) on reflection in L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the images as P" and Q" respectively.
(iv) State or describe a single transformation that maps P' onto P".