Introduction to Reflection

Q.

The coordinate notation shows how the coordinate of a figure are related to the coordinates of its image after transformations. What are the transformations? Are the figure and its image congruent? Explain.

$(\mathrm{x},\mathrm{y})\to (2\mathrm{x}+4,2\mathrm{y}-3)$

Q.

Find the fourth proportion in each of the following:

$21,27,14$

Q. In which of the following transformations does the shape and the size of the object change?

1. Rotation
2. Dilation
3. Translation
4. Reflection

Q.

The vertices of a rectangle are $\mathrm{Q}(-6,2),\mathrm{R}(6,2),\mathrm{S}(6,-4)$ and $\mathrm{T}(-6,-4)$. Dilate the rectangle with respect to the origin using a scale factor of $\frac{3}{2}$.Then translate it $5$ units right and $1$ unit down. What are the coordinate of image?

Q.

What is meant by transformations of functions?

Q. If $12:16$ and $21:p$ are proportional to one another, then find the value of $p$.

1. $35$
2. $20$
3. $24$
4. $28$

Q. Which of the following sequence of transformations relates all the four triangles in the figure given below?

1. $JKL\stackrel{\text{Reflection along the x-axis}}{\to }ACB\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }GHI$
2. $ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the x-axis}}{\to }DEF$
3. $DEF\stackrel{\text{Reflection along the y-axis}}{\to }JKL\stackrel{\text{Reflection along the y-axis}}{\to }GHI\stackrel{\text{Reflection along the y-axis}}{\to }ACB$
4. $GHI\stackrel{\text{Reflection along the y-axis}}{\to }DEF\stackrel{\text{Reflection along the y-axis}}{\to }ACB\stackrel{\text{Reflection along the x-axis}}{\to }JKL$

Q. Figure 1 is dilated with a scale factor of $0.5$ about the origin to get figure 2. The length of b is $26.7cm$ and the length of f is $10cm.$ The perimeter of figure 1 is $76.2cm$. Find the value of d.

1. $7.5cm$
2. $23.35cm$
3. $13.35cm$
4. $14.75cm$

Q.

Which transformations are rigid transformations?

1. dilation

2. reflection

3. rotation

4. stretch

5. translation

Q. Rectangle ABCD is reflected along the y-axis and translated by $8$ inches in the upward direction to give image EFGH. If the length of AB is $12$ inches and that of FG is $8$ inches, then what is the perimeter of EFGH?

1. $40in$
2. $48in$
3. $16in$
4. $20in$

Q. Your friend wanted to adjust the position of the birthday banner from ABC to A'B'C'. Help him identify the transformation required to set the banner.

1. Translation
   
2. Reflection
   
3. Rotation
   
4. None of these
   

Q. What is the degree of rotation from the center of a spinning wheel after undergoing rotation transformation in the clockwise direction?

1. ${180}^o$
2. ${360}^o$
3. ${90}^o$
4. ${270}^o$

Q. Which of the following transformations is applied to the position of the red mirror to get the blue mirror?

1. Translation
2. None of the above
3. Rotation
4. Reflection

Q. If the model of a square box is dilated about the origin by the scale factor of $2$. What are the resultant coordinates of the image?

1. $A^{\prime }(-1,0),B^{\prime }(1,0),C^{\prime }(1,2),D^{\prime }(-1,2)$
2. $A^{\prime }(0,0),B^{\prime }(2,0),C^{\prime }(2,2),D^{\prime }(0,2)$
3. $A^{\prime }(1,0),B^{\prime }(3,0),C^{\prime }(1,2),D^{\prime }(3,2)$
4. $A^{\prime }(-0.5,-0.5),B^{\prime }(-1.5,-0.5),C^{\prime }(-0.5,1.5),D^{\prime }(1.5,1.5)$

Q. Find the coordinates of image $\overline{PQ}$ under reflection about the $y$-axis, where $P(3,2)$ and $Q(1,0)$.

1. $P^{\prime }(3,2),Q^{\prime }(-1,0)$
2. $P^{\prime }(-3,2),Q^{\prime }(-1,0)$
3. $P^{\prime }(-3,-2),Q^{\prime }(-1,0)$
4. $P^{\prime }(3,-2),Q^{\prime }(1,0)$

Q. This is the resulting picture of a flag after getting dilated about the origin by a scale factor of $0.5$. What are the initial coordinates of the flag?

1. $A(8,4),B(20,12),C(8,12)$
2. $A(8,8),B(20,6),C(8,12)$
3. $A(8,8),B(20,12),C(8,12)$
4. $A(8,8),B(20,12),C(8,6)$

Q. Rock designed a logo by transforming ABCD to get A'B'C'D' as shown below. Identify the transformation performed by Rock.

1. Reflection over the line $x=0$
2. Translation of 1 unit toward the right
3. Reflection over the line $y=0$
4. Rotation of ${90}^{\circ }$ about the origin in the clockwise direction

Q. What transformations should figure $1$ undergo to join figure $2$ to form a square?

1. Reflection on the $y$-axis $\to$ Translation of three units toward the left $\to$ Translation of two units up $\to$ Dilation about the origin with a scale factor of $2$
2. Rotation of ${90}^o$ clockwise about the origin $\to$ Translation of three units up $\to$ Translation of three units toward the left $\to$ Dilation about the origin with a scale factor of $2$
3. Dilation about the origin with a scale factor of $2\to$ Translation of two units up $\to$ Translation of three units toward the left
4. Dilation about the origin with a scale factor of $2\to$ Rotation of 90° counterclockwise about the origin $\to$ Translation of three units toward the left $\to$ Translation of two units up

Q. Identify the transformation that occurs from $\Delta ABC$ to $\Delta DEF$ and the correct congruence relation between the triangles.

1. Reflection along the $y$-axis, $\Delta EFD\cong \Delta BCA$
2. Clockwise rotation of $90°$ about the origin, $\Delta ABC\cong \Delta DEF$
3. Reflection along the $y$-axis, $\Delta DEF\cong \Delta ACB$
4. Rightward translation by $6$ units, $\Delta FED\cong \Delta BAC$

Q. What transformations $△ABC$ require to join with $△EDF$ to form a rectangle?

1. Rotation, reflection
2. Translation, dilation
3. Translation, rotation
4. Reflection, translation

Q. The four vertices of a mobile are: \(A(5, −10), B(8, −10), C(8, −6)\) and \(D(5, −6).\) If we try to see them through a magnifying glass, the new vertices would be \(A(7.5, −15), B(12, −15), C(12, −9), \) and \(D(7.5, −9)\). What is the factor by which the image of the mobile is magnified?

Q. Find the sequence of transformations for the given figure.

1. Dilation of $ABCD$ about the origin with a scale factor of $2$; Dilation of $EFGH$ about the origin with a scale factor of $0.5$, rotation of ${180}^{\circ }$ clockwise about the origin
   
2. Dilation of $ABCD$ about the origin with a scale factor of $2$, rotation of ${180}^{\circ }$ clockwise about the origin; Dilation of $EFGH$ about the origin with a scale factor of $0.5$, rotation of ${180}^{\circ }$ clockwise about the origin
   
3. Dilation of $ABCD$ about the origin with a scale factor of $2,$ rotation of ${180}^{\circ }$ clockwise about the origin; Dilation of $EFGH$ about the origin with a scale factor of $0.5$
   
4. Dilation of $ABCD$ about the origin with a scale factor of $0.5$; Dilation of $EFGH$ about origin with a scale factor of $2$, rotation ${180}^{\circ }$ clockwise about the origin
   

Q. The position of lawn $ABC$ is transformed and a new image is formed. What type of transformation is it?

1. Reflection
2. Rotation
3. Translation
4. Dilation

Q. Can we say that the transformation in figure 1 is the same as in figure 2? Identify the type of transformation that both the figures will undergo.

1. No, Figure 1: Translation, Figure 2: Reflection
   
2. No, Figure 1: Reflection, Figure 2: Rotation
   
3. Yes, Figure 1 and figure 2: Rotation
   
4. Yes, Figure 1 and figure 2: Reflection
   

Q. In which of the following transformations, a figure is flipped over a fixed line to obtain the transformed figure?

1. Translation
2. Reflection
3. Rotation
4. None of the above

Q. What transformations figures $1$ and $2$ require to form figure $3$?

1. Figure 1: Rotation ${180}^o$ counterclockwise about the origin, translation;
   Figure 2: Dilation about the origin with a scale factor of $0.5$, reflection on the y-axis, translation
2. Figure 1: Rotation ${90}^o$ clockwise about the origin, translation;
   Figure 2: Dilation about the origin with a scale factor of $0.5$, reflection on the y-axis, translation
3. Figure 1: Rotation ${90}^o$ counterclockwise about the origin, translation;
   Figure 2: Dilation about the origin with a scale factor of $2$, reflection on the y-axis, translation
4. Figure 1: Rotation ${90}^o$ counterclockwise about the origin, translation;
   Figure 2: Dilation about the origin with a scale factor of $0.5$, reflection on the y-axis, translation

Q. $ABCD$, a square, is dilated about the origin. If the scale factor is $0.5$, what are the coordinates of the resultant image $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$?

1. $A^{\prime }(0.25,0.25),B^{\prime }(1.5,0.25),C^{\prime }(1.5,1.5),D^{\prime }(0.25,1.5)$
2. $A^{\prime }(3,3),B^{\prime }(1.5,3),C^{\prime }(1.5,1.5),D^{\prime }(3,1.5)$
3. $A^{\prime }(0.5,0.5),B^{\prime }(1.5,0.5),C^{\prime }(1.5,1.5),D^{\prime }(0.5,1.5)$
4. $A^{\prime }(2,2),B^{\prime }(6,2),C^{\prime }(6,6),D^{\prime }(2,6)$