Exercise 4.3 - Chapter 4 - Geometry - Term 3 - 7th Maths Guide Samacheer Kalvi Solutions

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Ex $4.3$
Miscellaneous Practice problems
Question $1 .$
The bishop, in given picture of chess board, can move diagonally along dark squares. Describe the translations of the bishop after two moves as shown in the figure.

Solution:
For first: $2 \rightarrow, 2 \downarrow$; For second move: $5 \leftarrow, 5 \downarrow$
 

Question $2 .$
Write a possible translation for each of chess piece for a single move.

Solution:
Pawn $-1 \uparrow$ or $2 \uparrow$
Rook $-1$ to $8 \uparrow$
Knight $-2 \rightarrow, 1$ for $2 \leftarrow, 1 \uparrow$ or $1 \rightarrow, 2$ ๆor $1 \leftarrow, 2 \uparrow$

Bishop $-1 \rightarrow, 1 \uparrow$ or $2 \rightarrow, 2 \uparrow$ or $3 \rightarrow, 3 \uparrow$ or $4 \rightarrow, 4 \uparrow$ or $5 \rightarrow 5 \uparrow 1 \leftarrow, 1 \uparrow$ or $2 \leftarrow, 2 \uparrow$ or $3 \leftarrow, 3 \uparrow$ or $4 \leftarrow, 4 \uparrow$ or $5 \leftarrow 5 \uparrow$ Queen $-1$ to $8,1 \rightarrow, 1 \uparrow$ or $2 \rightarrow, 2 \uparrow$ or $3 \rightarrow, 3$ for $4 \rightarrow, 4$ for $5 \rightarrow, 5$ for $1 \leftarrow, \uparrow 1$ or $2 \leftarrow, 2$ ๆor $3 \leftarrow 3 \uparrow$ or $4 \leftarrow, 4 \uparrow$ or $5 \longleftarrow 5 \uparrow$
King $-1 \rightarrow$ or 4 or $\uparrow$
 

Question 3 .
Referring the graphic given, answer the following questions. Each bar of the category is made up of boy-girl-boy unit, (i) Which categories show a boy-girl-boy unit that is translation within the bar? (ii) Which categories show a boy-girl-boy unit that is reflected within the bar?

Solution:
(i) Essay Writing category shows translation
(ii) Essay Writing and Mono Acting categories shows reflection
 

Question $4 .$
Given figure is a floor design in which the length of the small red equilateral triangle is $30 \mathrm{~cm}$. All the triangles and hexagons are regular. Describe the translations in $\mathrm{cm}$, represented by the (i) yellow line (ii) black line (iii) blue line.

Solution:
(i) $120 \mathrm{~cm} \rightarrow, 210 \mathrm{~cm} \downarrow$
(ii) $270 \mathrm{~cm} \leftarrow, 330 \mathrm{~cm} \uparrow$
(iii) $150 \mathrm{~cm} \rightarrow$
 

Question $5 .$
Describe the transformation involved in the following pair of figures (letters). Write translation, reflection or rotation.

Solution:
(i) rotation
(ii) reflection
(iii) translation
(iv) reflection
(v) rotation
(vi) reflection
(vii) rotation
(viii) translation
 

Challenge problems
Question 1.
In chess, a knight can move only in an L-shaped pattern:

- two vertical squares, then one horizontal square;
- two horizontal squares, then one vertical square;
- one vertical square, then two horizontal squares; or
- one horizontal square, then two vertical squares.

Write a series of translations to move the knight from g8 to g5 (at most two moves)
Solution:
$2 \leftarrow, 1 \downarrow$ and then $1 \leftarrow, 2 \downarrow$ (or) $2 \leftarrow, 1 \downarrow$ and then $1 \leftarrow, 2 \downarrow$
 

Question $2 .$
The pink shape is congruent to blue shape. Describe a sequence of transformations in which the blue shape is the image of pink shape.

Solution:
(i) Translation $3 \leftarrow, 5 \uparrow$ and $90^{\circ}$ counter clockwise rotation about the green point and translates $5 \leftarrow, 2 \downarrow$,
(ii) Translation $2 \leftarrow 90^{\circ}$ counter clockwise rotation about the green point and translates $2 \leftarrow, 2 \downarrow$.
 

Question $3 .$

Solution:

Question $4 .$
Draw concentric circles given that radius of inner circle is $4.5 \mathrm{~cm}$ and width of circular ring is $2.5 \mathrm{~cm}$.
Solution:
Give radius of inner circle $=4.5 \mathrm{~cm}$
Width of circular ring is $2.5 \mathrm{~cm}$
Radius of outer circle $=4.5+2.5=7 \mathrm{~cm}$

Step 1: Drawn a rough diagram and marked the given measurements
Step 2 : Taken any point $O$ and marked it as the center.
Step 3 : With $\mathrm{O}$ as center and drawn a circle of radius $\mathrm{OA}=4.5 \mathrm{~cm}$.
Step 4 : With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OB}=4.5+2.5=7 \mathrm{~cm}$. Thus the concentric circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}$
$=7-4.5=2.5 \mathrm{~cm}$
 

Question $5 .$
Draw concentric circles given that radius of outer circle is $5.3 \mathrm{~cm}$ and width of circular ring is $1.8 \mathrm{~cm}$.
Solution:
Give radius of outer circle $=5.3 \mathrm{~cm}$
Width of circular ring $=1.8 \mathrm{~cm}$
Radius of the inner circle $=5.3-1.8$
$=3.5 \mathrm{~cm}$

Step 1: Drawn a rough diagram and marked the given measurements
Step 2 : Taken any point $\mathrm{O}$ and marked it as the center.
Step 3: With $\mathrm{O}$ as center drawn a circle of radius $\mathrm{OA}=3.5 \mathrm{~cm}$.
Step 4 : With $\mathrm{O}$ as center, drawn a circle of radius $\mathrm{OB}=5.3 \mathrm{~cm}$. Thus concentric circles $C_{1}$ and $C_{2}$ are drawn.
Width of the circular ring $=\mathrm{OB}-\mathrm{OA}$
$=5.3-3.5=1.8 \mathrm{~cm}$