Question 1: Use graph paper for this question. Plot the points A (8, 2) \ and \ B (6, 4) . These points are the vertices of a figure which is symmetrical about x = 6 \ and \  y = 2 . Complete the figure on the graph. Write down the geometrical name of the figure.   [2000, 2006]

Answer:

sy1

Name of the geometrical figure is a square as all the sides are equal and parallel.

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Question 2: Use graph paper for this question. Use 2 cm = 1 unit on both the axes. Plot the points A (-2, 4), B (2, 1) \ and \ C (-6, 1) .

(i) Draw the line of symmetry of \triangle ABC .

(ii) Mark the point D  if the line in (i) and the line BC  are both lines of symmetry of the quadrilateral ABCD . Write down the co-ordinates of point D .

(iii) What kind of quadrilateral is figure ABCD ?

(iv) Write down the equation of BC and the line of symmetry named in (i.)   [1996]

Answer:

sy2.jpg

(i) The dotted line is the line of symmetry. The equation of that line is y = 1 \ and \ x = -2 

(ii) Coordinates of point D = (-2, -2)

(iii) It is a Rhombus.

(iv) The equation of that line is y = 1 \ and \  x = -2

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Question 3: Use graph paper for this question A (0, 3), B (3, -2) \ and \ O (0, 0) are the vertices of \triangle ABO .

(i) Plot D the reflection of B in the y-axis , and write its co-ordinates.

(ii) Give the geometrical name of the figure ABOD .

(iii) Write the equation of the line of symmetry of the line ABOD .   [2010]

Answer:

sy3.jpg

(i)  Plotted above

(ii) The coordinates of D (-3, -2)

(iii) Arrow Head

(iv) x = 0 is the equation of line of symmetry

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Question 4: Using graph paper and taking 1 cm = 1 unit along both x \ and \ y axis .

(i) Plot the points A (-4, 4) \ and \ B (2, 2) .

(ii) Reflect A \ and \ B in the origin to get the images A' \ and \ B' respectively.

(iii) Write down the co-ordinates of A' \ and \ B' .

(iv) Give the geometrical name for the figure ABA'B' .

(v) Draw and name its lines of symmetry.   [2012]

Answer:

sy4.jpg

(i) Plotted above.

(ii) Marked A' \ and \ B'

(iii) A'(-4, 4) \ and \ B'(-2, -2) 

(iv) Lines of symmetry are y = x \ and \ y = -x

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Question 5: Use graph paper to answer the following questions. (take 2 cm = 1 unit on both the axes)

(i) Plot the points A (-4, 2)  and B (2, 4) .

(ii) A'  is the images of A 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 geometrical name of the figure ABA'B' 

(v) Name a line of symmetry of the figure formed.   [2014]

Answer:

sy5.jpg

(i) Plotted above

(ii) A'(4, 2)

(iii) B'(2,0)

(iv) The figure is a kite

(v) y=2 is a line of symmetry

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