Mathematics
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.
Reflection
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Answer
(i) Since, x = 6 is a straight line parallel to y-axis and at a distance of 6 units from it, therefore in the figure, PQ represents x = 6.
Steps of construction :
Mark A(4, 5)on the graph.
From point A draw a straight line perpendicular to PQ and produce.
On this line mark a point A' which is at same distance behind PQ as A(4, 5) before it.
The graph is shown below:
From graph,
A' = (8, 5).
Hence, co-ordinates of A' = (8, 5).
(ii) Since, x = -5 is a straight line parallel to y-axis and at a distance of 5 units from it, therefore in the figure, PQ represents x = -5.
Steps of construction :
Mark B(-3, 2)on the graph.
From point B draw a straight line perpendicular to PQ and produce.
On this line mark a point B' which is at same distance behind PQ as B(-3, 2) before it.
The graph is shown below:
From graph,
B' = (-7, 2).
Hence, co-ordinates of B' = (-7, 2).
(iii) Since, y = -2 is a straight line parallel to x-axis and at a distance of 2 units from it, therefore in the figure, PQ represents y = -2.
Steps of construction :
Mark C(3, 6)on the graph.
From point C draw a straight line perpendicular to PQ and produce.
On this line mark a point C' which is at same distance behind PQ as C(3, 6) before it.
The graph is shown below:
From graph,
C' = (3, -10).
Hence, co-ordinates of C' = (3, -10).
(iv) Since, y = 5 is a straight line parallel to x-axis and at a distance of 5 units from it, therefore in the figure, PQ represents y = 5.
Steps of construction :
Mark D(-2, -5)on the graph.
From point D draw a straight line perpendicular to PQ and produce.
On this line mark a point D' which is at same distance behind PQ as D(-2, -5) before it.
The graph is shown below:
From graph,
D' = (-2, 15).
Hence, co-ordinates of D' = (-2, 15).
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Related Questions
Use graph paper to answer the following questions. (Take 2 cm = 1 unit)
(i) Plot the points A(-4, 2) and B(2, 4).
(ii) A' is the image of A when reflected in the y-axis. Plot it on the graph paper and write the co-ordinates of A'.
(iii) B' is the image of B when reflected in the line AA'. Write the co-ordinates of B'.
(iv) Write the geometric name of the figure ABA'B'.
(v) Name a line of symmetry of the figure formed.
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'.
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.
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.