Q3 Math 8 Benchmark Review "The Covid Edition"

Q3 Math 8 Benchmark Review "The Covid Edition"

Translation

•  A transformation that SLIDES a figure along a straight line.

• Produces an image that is CONGRUENT to the original image with the SAME ORIENTATION

• Translate RIGHT: (x, y) → (x + a, y)

• Translate LEFT: (x, y) → (x - a, y)

• Translate UP: (x, y) → (x, y + b)

• Translate DOWN: (x, y) → (x, y - b)

Reflection

• A transformation that FLIPS a figure across a line called the LINE OF REFLECTION.

• Produces a MIRROR image that is CONGRUENT to the original image

• Reflect across the x-axis: (x, y) → (x, -y)

• Reflect across y-axis: (x, y) → (-x, y)

Multiple Choice

Which of the statements is TRUE about  $\Delta U'V'W'$ ? 

•   $\Delta U'V'W'$ is a translation of  $\Delta UVW$  

•   $\Delta U'V'W'$  is a reflection of  $\Delta UVW$  over the x-axis

•   $\Delta U'V'W'$ is a  $90\degree$  counterclockwise rotation of  $\Delta UVW$  

•  $\Delta U'V'W'$  is a reflection of  $\Delta UVW$  over the y-axis

Rotation

• A transformation that TURNS a figure around a given point called the center of rotation.

• Produces an image that is CONGRUENT to the original image, but with a DIFFERENT ORIENTATION

• Clockwise rotates to the RIGHT

• Counterclockwise rotates to the LEFT

• 90° clockwise: (x, y) → (y, -x)

• 90° counterclockwise: (x, y) → (-y, x)

• 180°: (x, y) → (-x, -y)

  
  

Multiple Choice

Figure $S'T'U'V'W'$  is a  $180\degree$  rotation of  $STUVW$  

• TRUE

• FALSE

Multiple Choice

Which of the following describes the transformation shown? 

•  $90\degree$  clockwise rotation

•  $90\degree$  counterclockwise rotation

•  $180\degree$  rotation

• Reflection across the x-axis

• Reflection across the y-axis

Dilation

• A transformation that results in a CHANGE in SIZE of a figure

• Produces a figure that is SIMILAR, but NOT CONGRUENT to the original image

• SCALE FACTOR  $\left(k\right)$  multiplies the figure

•  $k>1$  results in an ENLARGEMENT

•  $k<1$  results in a REDUCTION

•  $\left(x,y\right)\rightarrow\left(kx,ky\right)$  

Multiple Choice

Figure B is the dilated image of Figure A. What scale factor was used to produce Figure B?

• $k=2$

• $k=\frac{1}{2}$

• $k=5$

• $k=\frac{1}{5}$

Multiple Choice

Which of the following statements shows that figure A and figure B are similar?

• A translation of figure A  3 units left and 6 units down

• A reflection of figure A over the y-axis, then a translation down 6 units.

• A dilation of figure A with a scale factor of 2.

• A dilation of figure A with a scale factor of  $\frac{1}{2}$  .

Multiple Select

Which of the following transformations will result in an image that is CONGRUENT to the original pre-image? Choose ALL that apply.

• dilation

• reflection

• rotation

• translation

Multiple Choice

Line segment CD was reflected over the x-axis to create line segment EF. Line segment EF was translated 5 units down to create line segment GH. Which of the following statements is TRUE.

• Line segment GH is shorter that line segment EF

• Line segment CD is longer that line segment EF

• Line segment GH is the same length as line segment AB

• Not enough information is provided

Multiple Select

 $\Delta ABC$ is a right triangle. Which of the following are true about the  $90\degree$ angle? Choose ALL that apply.

• If it is rotated  $90\degree$ clockwise it will no longer measure  $90\degree$  

• If it is reflected over  $y=x$ it will still measure  $90\degree$  

• If it is translated 5 units up it will no longer measure  $90\degree$  

• If it is translated 2 units right, it will still measure  $90\degree$  

• If it is reflected over the y-axis it will still measure  $90\degree$  

Multiple Choice

 $\Delta STU$  is translated 5 units left, then reflected over the x-axis resulting in  $\Delta S'T'U'$ . What is the location of vertex  $S'?$  

•  $\left(4,-5\right)$  

•  $\left(-5,4\right)$  

•  $\left(-4,5\right)$  

•  $\left(5,-4\right)$  

Multiple Choice

The figures shown are congruent. Which sequence of transformations can be used to prove they are congruent?

• A translation 5 units right, then 3 units down.

• A reflection over the x-axis, followed by a $90\degree$ clockwise rotation.

• A $360\degree$ rotation, followed by a reflection over the y-axis.

• A reflection over the y-axis, followed by a translation 1 unit right and 3 units down.

Multiple Select

Square ABCD was drawn on the coordinate plane. It was reflected over the x-axis, dilated by a scale factor of $\frac{1}{3}$  , and finally rotated clockwise to create square A'B'C'D'.  Which of the following statements are TRUE about the two squares.

• They are congruent.

• They are not congruent.

• They are similar.

• They are not similar.

• Cannot be determined since no coordinates are given.

Multiple Select

Which of the following sequences of transformations will produce an image that is SIMILAR, but has a LARGER area than the original image, shown. Choose ALL that apply.

• A reflection over the x-axis and a rotation of $90\degree$ clockwise

• A translation 2 units left and a dilation about the origin with a scale factor of $\frac{5}{6}$

• A dilation about the origin with a scale factor of $\frac{8}{5}$ followed by a reflection over $y=x$

• A rotation of $180\degree$ followed by a dilation about the origin with a scale factor of 1

• A reflection over the y=axis followed by a dilation about the origin with a scale factor of 3

Multiple Select

A sequence of transformations is performed on $\Delta ABC$ .  Which of the following will result in a triangle that is SMALLER in area, but SIMILAR to the original image? Choose ALL that apply.

• A  $90\degree$  clockwise rotation followed by a dilation with a scale factor of  $\frac{5}{4}$  

• A dilation with a scale factor of  $\frac{2}{3}$  followed by a translation 2 units left, and finally a dilation with a scale factor of  $\frac{1}{2}$  

• A reflection over the x-axis, followed by a rotation of  $360\degree$  

• A reflection over the y-axis, then a dilation with a scale factor of  $\frac{7}{8}$  

Fill in the Blanks

Multiple Choice

Which of the sequences below can be used to describe the transformation of $A\ to\ A'\ to\ A''?$  

 

• A  $90\degree$  clockwise rotation, followed by a reflection over the x-axis.

• A translation up, followed by a  $90\degree$  counterclockwise rotation. 

• A reflection over the x-axis, followed by a reflection over the y-axis.

• A  $90\degree$  counterclockwise rotation, followed by a reflection over the y-axis.

Multiple Choice

A rectangle is drawn on the coordinate plane. It is rotated $180\degree,$ 

translated 5 units up, and finally reflected over the y-axis.  Which of the following statements is TRUE about the resulting figure?

• It is larger than the original

• It is congruent to the original

• It has a different shape than the original

• It is smaller than the original