Mathematics
The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A".
(i) Write down the co-ordinates of A".
(ii) Write down a single transformation that maps A onto A".
Reflection
5 Likes
Answer
(i) Reflection in origin is given by,
Mo(x, y) = (-x, -y)
∴ Image on reflection of A(4, 6) in origin = A'(-4, -6)
Reflection in y-axis is given by,
My(x, y) = (-x, y)
∴ Image on reflection of A'(-4, -6) in y-axis = A"(4, -6)
Hence, co-ordinates of A" = (4, -6).
(ii) Transformation from A to A" is,
A(4, 6) = A"(4, -6).
Reflection in x-axis is given by,
Mx(x, y) = (x, -y)
∴ Image on reflection of A(4, 6) in x-axis = A"(4, -6)
Hence, the single transformation that maps A onto A" is reflection in x-axis.
Answered By
2 Likes
Related Questions
Using a graph paper, plot the points A(6, 4) and B(0, 4).
(i) Reflect A and B in the origin to get images A' and B'.
(ii) Write the coordinates of A' and B'.
(iii) State the geometrical name for the figure ABA'B'.
(iv) Find its perimeter.
Use graph paper for this question.
Plot the points O(0, 0), A(-4, 4), B(-3, 0) and C(0, -3).
(i) Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
(ii) Name the figure OABCB'A'.
Use a graph paper for this question (take 2 cm = 1 unit on both x and y axes).
(i) Plot the following points : A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
(ii) Reflect points B, C, D on y-axis and write down their coordinates. Name the images as B', C', D' respectively.
(iii) Join points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation of line of symmetry of the figure formed.
Use a graph paper for this question taking 1 cm = 1 unit along both the x-axis and the y axis.
(i) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, -2), E(2, -5) and F(0, -5).
(ii) Reflect the points B, C, D and E on the y-axis and name them B', C', D' and E' respectively.
(iii) Write the co-ordinates of B', C', D' and E'.
(iv) Name the close figure formed.