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'.
Use graph sheet for this question.
(a) Plot A(0, 3), B(2, 1) and C(4, -1).
(b) Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
(c) Reflect point A in the line BB' and name its images as A'.
(d) Plot and write coordinates of point A'.
(e) Join the points ABA'B' and give the geometrical name of the closed figure so formed.
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.