Mathematics
On a graph, plot A(4, 6) and B(2, 3). Find the image of A when reflected in the line y = 0, name it A'. Find the co-ordinates of B', the image of B when reflected in the line AA'.
Give a geometrical name for the figure AB'A'B. Calculate the area of the figure AB'A'B.
Reflection
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Answer
Points A(4, 6) and B(2, 3) are plotted on the graph below:
Line y = 0 is the equation of x-axis.
Reflect point A in x-axis.
From graph we get,
The coordinates of point A' = (4, -6)
Reflect point B in line AA'.
From graph we get,
The coordinates of point B' = (6, 3)
Join points AB'A'B.
From graph we get,
AB'A'B formed is a kite.
Area of kite
= × 12 × 4
= 24 sq.units.
Hence, the area of kite 24 sq.units.
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Related Questions
Use graph paper for this question (Take 2 cm = 1 unit along both x and y axis). ABCD is a quadrilateral whose vertices are A(2, 2), B(2, -2), C(0, -1) and D(0, 1).
(i) Reflect quadrilateral ABCD on the y-axis and name it as A'B'C'D'.
(ii) Write down the co-ordinates of A' and B'.
(iii) Name two points which are invariant under the above reflection.
(iv) Name the polygon A'B'C'D'.
Find the image of the following points as directed.
(i) Point A(4, 5) reflected in the line x = 6.
(ii) Point B(-3, 2) reflected in the line x = -5.
(iii) Point C(3, 6) reflected in the line y = -2.
(iv) Point D(-2, -5) reflected in the line y = 5.
Use graph paper for this question. Take 1 cm = 1 unit on both x and y axes.
(i) Plot the following points on your graph sheets : A(-4, 0), B(-3, 2), C(0, 4), D(4, 1) and E(7, 3).
(ii) Reflect the points B, C, D and E on the x-axis and name them as B', C', D' and E' respectively.
(iii) Join the points A, B, C, D, E, E', D', C', B' and A in order.
(iv) Name the closed figure formed.
Use a graph paper for this question. Take 2 cm = 1 unit along both the axes.
(i) Plot the points A(0, 4), B(2, 2), C(5, 2) and D(4, 0). E(0, 0) is the origin.
(ii) Reflect B, C, D on the y-axis and name them as B', C' and D' respectively.
(iii) Join the points ABCD D'C'B' and A in order and give a geometrical name to the closed figure.