ICSE Board Problems, Symmetry

Class 10: Symmetry – ICSE Board Problems

Date: October 14, 2017Author: ICSE CBSE ISC Board Mathematics Portal for Students 0 Comments

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:

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:

(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:

(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:

(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:

(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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