We included **HMH Into Math Grade 8 Answer Key**** PDF** **Module 2 Transformations and Similarity **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 2 Answer Key Transformations and Similarity

**Do You Haul Bones?**

A museum received a crate containing a set of dinosaur bones. You need to move the crate from its current location to the location marked on the grid. Each unit on the grid represents 1 meter.

How could you use a sequence of transformations to haul the crate to its new location?

**Turn and Talk**

Why might the museum not want you to use a reflection to move the crate?

**Are You Ready?**

**Complete these problems to review prior concepts and skills you will need for this module.**

**Polygons in the Coordinate Plane**

**Determine the length, in units, of each side of the figure on the coordinate plane**.

Question 1.

\(\overline{L M}\) ________

Answer:

7 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}L(-4, -3), M(-4, 4)

SQRT (-4 – (-4))^{2} + (4 – (-3))^{2}

SQRT (-4 + 4)^{2} + (4 + 3)^{2}

SQRT (0)^{2} + (7)^{2}

\(\sqrt{0 + 49}\)

\(\sqrt{49}\) = 7 units.

Question 2.

\(\overline{M N}\) ________

Answer:

3 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}N(-1, 4), P(-1, 1)

SQRT{(-1 – (-1))^{2} + (1 – 4))^{2}}

SQRT {0 + (-1 + 4)^{2}}

SQRT {(3)^{2}}

\(\sqrt{9}\) = 3 units.

Question 3.

\(\overline{N P}\) ________

Answer:

3 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}N(-1, 4), P(-1, 1)

SQRT{(-1 – (-1))^{2} + (1 – 4))^{2}}

SQRT {0 + 3^{2} }

SQRT {(3)^{2}}

\(\sqrt{9}\) = 3 units.

Question 4.

\(\overline{P Q}\) ________

Answer:

6 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}P(-1, 1) , Q(5, 1),

SQRT{(5 – (-1))^{2} + (1 – 1))^{2}}

SQRT {(5 + 1)^{2} + 0}

SQRT {(6)^{2} + (0)^{2}}

\(\sqrt{36 + 0}\)

\(\sqrt{36}\) = 6 units.

Question 5.

\(\overline{Q R}\) ________

Answer:

4 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}Q(5, 1) , R(5, -3),

SQRT{(5 – 5)^{2} + (-3 – 1))^{2}}

SQRT {(0)^{2} + (4)^{2}}

\(\sqrt{0 + 16}\)

\(\sqrt{16}\) = 4 units.

Question 6.

\(\overline{P Q}\) ________

Answer:

6 units,

Explanation:

The distance between the points (x1, y1) and (x2, y2) is given by the formula,

SQRT (x2 – x1)^{2} + (y2 – y1)^{2
}R(5, -3) , S(-4, -3),

SQRT{((-4) – 5)^{2} + (-3 + 3))^{2}}

SQRT {(-4 – 5)^{2} + 0}

SQRT {(-9)^{2} + (0)^{2}}

\(\sqrt{81}\)

\(\sqrt{81}\) = 9 units.

**Scale Drawings**

A scale drawing of a school cafeteria has a scale of 1 inch : 4 feet. Use this information to answer each question.

Question 7.

In the drawing, the cafeteria dining room has a length of 18 inches. What is the actual length of the dining room?

Answer:

72 feet,

Explanation:

The cafeteria dining room has a length of 18 inches.

length = 18 inches

The actual length of the dining room,

18 x 4 = 72 feet

Question 8.

The actual width of the cafeteria kitchen is 42 feet. What is the width of the kitchen in the scale drawing?

Answer:

10.5 inches,

Explanation:

The actual width of the cafeteria kitchen is 42 feet,

the width of the kitchen in the scale drawing.

42/4 = 10.5 inches

**Translations, Reflections, and Rotations**

**Draw the image of each transformation on the coordinate plane.**

Question 9.

Rotate Triangle ABC 180° about the origin.

Answer:

Explanation:

The rule for a rotation by 180° about the origin is (x, y)→(−x,−y)

A(-1, 4) → A'(1,−4)

B(5, 2) → B'(-5,−2)

C(2, 1) → C'(-2,−1)

Question 10.

Reflect Triangle DEF across the y-axis, and then translate it 4 units down.

Answer:

Explanation:

In fig (a) the triangle is reflected to right side

The rule for a reflection over the y -axis is,

**(x, y)→(−x, y)**

D(-4, 1)→ D'(4, 1)

E(-3, 5)→ E'(3, 5)

F(-2, 1)→ F'(2, 1)

In fig (b) the triangle is shifted down to 4 units down.

subtract 4 from ‘y’ value, then

**(x, y – 4)→(−x, y)**

D'(4, 1 – 4) → D'(4, -3)

E'(3, 5 – 4) → E'(3, 1)

F'(2, 1 – 4) → F'(2, -3)