We included HMH Into Math Grade 8 Answer Key PDF Module 1 Review to make students experts in learning maths.

Vocabulary

image
preimage
reflection
rotation
translation

For Problems 1—5, choose the correct term from the vocabulary box.

Question 1.
A(n) ____ is a transformation that slides a figure.
A translation is a transformation that slides a figure.
Explanation:
A translation is a type of transformation that takes each point in a figure,
and slides it the same distance in the same direction. Question 2.
A(n) ___ is a transformation that flips a figure across a line.
A reflection is a transformation that flips a figure across a line.
Explanation:
A reflection is known as a flip which is a mirror image of the shape.
An image will reflect through a line, known as the line of reflection.
A figure is said to reflect the other figure,
then every point in a figure is equidistant from each corresponding point in another figure. Question 3.
A(n) ____ is a transformation that turns a figure about a point.
A rotation is a transformation that turns a figure about a point.
Explanation:
Rotation means the circular movement of an object around a center.
It is possible to rotate different shapes by an angle around the center point. Question 4.
A(n) ____ is the original figure in a transformation.
A preimage is the original figure in a transformation.
Explanation:
A transformation is a change in the position, size, or shape of a new geometric figure.
The preimage of a transformation is the shape before the transformation
The new figure is called the image and original figure is known as preimage. Question 5.
A(n) ____ is the resulting figure in a transformation.
An image is the resulting figure in a transformation.
Explanation:
A transformation is a change in the position, size, or shape of a new geometric figure.
The image of a transformation is the shape after the transformation. Concepts and Skills

Question 6.
Figure ABCD and its image, Figure FGHJ, are shown. Which transformation of Figure ABCD produced Figure FGHJ? A. vertical translation
B. horizontal translation
C. reflection across a vertical line
D. reflection across a horizontal line
C. reflection across a vertical line.
Explanation:
The transformation of Figure ABCD produced Figure FGHJ is a reflection across a vertical line,
as the lines of the image are symmetry.

Question 7.
Use Tools Describe a sequence of transformations you could use to show that Triangle DEF is congruent to Triangle JKL. State what strategy and tool you will use to answer the question, explain The strategy used here is rotation.
Explanation:
Here, the triangle DEF is the rotation of the triangle JKL.
So the strategy used here is rotation,
as rotation is a transformation that turns a figure into a point.

Question 8.
Triangle PQR has vertices P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up
to produce Triangle P’Q’R’. Complete the table. P’ = (-4, -1),
Q’ = (-2, -2),
R’ = (1, 1). Explanation:
As it is translated 6 units left and 3 units up to produce Triangle P’Q’R’. So the coordinates of P’Q’R’ is
P’ = (-4, -1),
Q’ = (-2, -2),
R’ = (1, 1). For Problems 9-10, draw the image of each transformation.

Question 9.
Rotate Triangle RST 180 about the origin. The rule for a rotation by 180° about the origin is (x, y)→(−x, −y) Explanation:
The coordinates of RST are
R = (-2, 4),
S = (3, 4),
T = (2, 1).
So by rotating the triangle RST 180 about the origin,
the signs of the coordinates will become opposite.
The rule for a rotation by 180° about the origin is (x, y)→(−x, −y).
R’ = (2, -4),
S’ = (-3, -4),
T’ = (-2, -1).

Question 10.
Translate Quadrilateral WXYZ 5 units right and 2 units down. Quadrilateral WXYZ 5 units right and 2 units down
(x, y) = (x+5, y-2)
W’ = (2, -4),
X’ =  (1, 2),
Y’ =  (4, 1),
Z’ =  (4, -3). Explanation:
Given the co-ordinates are,
W = (-3, -2),
X = (-4, 4),
Y = (-1, 3),
Z = (-1, -1).
And the translation coordinates are,
W’ = (-3+5, -2-2) = (2, -4),
X’ = (-4+5, 4-2) = (1, 2),
Y’ = (-1+5, 3-2) = (4, 1)
Z’ = (-1+5, -1-2) = (4, -3)

Question 11.
Side KN of Figure KLMN is parallel to Side LM. Figure KLMN is rotated 90° clockwise about Point P to produce Figure RSTU. Based on this information, select all statements that are true. A. $$\overline{S T}$$ is parallel to $$\overline{R U}$$.
B. ∠R has the same measure as ∠N.
C. $$\overline{R S}$$ is the same length as $$\overline{M N}$$.
D. Figure RSTU is congruent to Figure KLMN.
E. ∠T has the same measure as ∠M.
A, D, and E are true.

Explanation:
As the side KN of Figure KLMN is parallel to Side LM,
when the figure KLMN is rotated 90° clockwise about Point P to produce Figure RSTU.
By the property of rotation $$\overline{S T}$$ is parallel to $$\overline{R U}$$,
Figure RSTU is congruent to Figure KLMN and ∠T has the same measure as ∠M.
Hence, A, D and E are true.

Question 12.
An artist is designing a logo for a new company by reflecting Triangle ABC across a vertical line and then translating it up and to the right to produce Triangle DEF. Find each measure, measure of ∠D: ____°
length of $$\overline{E F}$$: ___ in.
length of $$\overline{D F}$$: ___ in. $$\angle{D}$$ = 75°,
length of $$\overline{E F}$$: 4 in.
length of $$\overline{D F}$$: 3 in.

Explanation:
Given the triangle ABC across a vertical line,
then translating it up and to the right to produced triangle DEF.
So the measurements of $$\angle{DEF}$$ is,
$$\angle{D}$$ = $$\angle{B}$$ = 75°,
length of $$\overline{E F}$$ = length of $$\overline{AC}$$: 4 in.
length of $$\overline{D F}$$ = length of $$\overline{BA}$$: 3 in.

Question 13.
The point (a, b) is reflected across the x-axis and then translated 4 units to the right. What are the coordinates of the image of the point?
A. (-a, b + 4)
B. (-a + 4, b)
C. (a, -b + 4)
D. (a + 4, -b)
Option(D)
The coordinates of the image of the point (a + 4, -b).

Explanation:
A reflection is known as a flip which is a mirror image of the shape.
An image will reflect through a line, known as the line of reflection.
A figure is said to reflect the other figure,
then every point in a figure is equidistant from each corresponding point in another figure.
The reflection of (a, b) across the x-axis by translating 4 units to the right is (a + 4, -b).

Question 14.
How many types of transformations did you study in this module? Name and define each of them.
There are four types of transformations in this module. Those are

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

Explanation:
1. Translation:
A translation transforms a figure by moving each point the same distance in the same direction.
2. Rotation:
The rotation of a figure involves rotation each point around a specified point by a certain number of degrees.
3. Reflection:
As the name implies, a reflection is a mirror image of a shape. An image that will reflect through a line is known as the reflection line.
4. Dilation:
A Dilation is changing the size of an object without changing it’s shape.

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