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

## HMH Into Math Grade 8 Module 1 Review Answer Key

**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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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

Answer:

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

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

\(\angle{D}\) = 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)

Answer:

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.

Answer:

There are four types of transformations in this module. Those are

- Translation
- Rotation
- Reflection
- 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.