This pattern is based on traditional Aztec print designs. Identify the original shapes and describe all the transformations you can see in the design.

Given, the pattern based on traditional Aztec print designs. We have to identify the original shapes and describe all the transformations we can see in the design. The image is the result of performing a transformation, and the preimage is the original that we perform the transformation. In a given pattern, the original or preimage shapes are triangles, squares and trapezia. Translation moves a point or shape in any direction with no change to size. Reflection flips a point or shape over a given line called the line of reflection or the mirror line. Rotation turns a shape about a fixed point through a determined number of degrees. The centre is called the point of rotation. In the given pattern, triangles, squares and trapezia are translated, rotated and reflected.

This pattern is based on traditional Aztec print designs. Would you consider this a tessellation? Justify your response.

Given, the pattern based on traditional Aztec print designs. Tessellation is an arrangement of shapes closely fitted together, especially of polygons in a repeated pattern without gaps or overlapping The image is the result of performing a transformation, and the preimage is the original that we perform the transformation. In a given pattern, the original or preimage shapes are triangles, squares and trapezia. Here, the given pattern is a tessellation because there is an overall basic pattern that repeats without overlapping.

Copy and complete the table below: Point Translation up 3 units Translation left 5 units Translation down 2 units and right 7 units Dilation by a scale factor of 4 about the origin 0 , 0 6 , 1 3 , - 2 - 4 , 7 - 8 , - 5

Translation- moves a point or shape in any direction with no change to size. Dilation- creates a bigger or smaller image than the original (pre-image). Here, Translation up 3 units- ( x , y ) → ( x , y + 3 ) Translation left 5 units- ( x , y ) → ( x - 5 , y ) Translation down 2 units and right 7 units- ( x , y ) → ( x + 7 , y - 2 ) Dilation by 4 units- ( x , y ) → ( 4 x , 4 y ) Thus, the completed table is given below. Point Translation up 3 units Translation left 5 units Translation down 2 units and right 7 units Dilation by a scale factor of 4 about the origin 0 , 0 0 , 3 - 5 , 0 7 , - 2 0 , 0 6 , 1 6 , 4 1 , 1 13 , - 1 24 , 4 3 , - 2 3 , 1 - 2 , - 2 10 , - 4 12 , - 8 - 4 , 7 - 4 , 10 - 9 , 7 3 , 5 - 16 , 28 - 8 , - 5 - 8 , - 2 - 13 , - 5 - 1 , - 7 - 32 , - 20

Graph the image of the triangleABCafter a dilation with a scale factor of13 centered at the origin

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 10

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This is the logo for the Subaru car company. "Subaru" is the Japanese name for the cluster of stars known as the Pleiades in English (part of the constellation Taurus). "Subaru" also means "united" in Japanese - this expresses the idea that five companies merged to form Fuji Heavy Industries (FRI), the parent company of Subaru. So the star logo represents both a play on words and how FRI considers itself a united cluster of companies.

Describe any congruence transformations that are visible in this logo.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 10

Question Image

This is the logo for the Subaru car company. "Subaru" is the Japanese name for the cluster of stars known as the Pleiades in English (part of the constellation Taurus). "Subaru" also means "united" in Japanese - this expresses the idea that five companies merged to form Fuji Heavy Industries (FRI), the parent company of Subaru. So the star logo represents both a play on words and how FRI considers itself a united cluster of companies.

Describe any similarity transformations that are visible in this logo.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 11

This pattern is based on traditional Aztec print designs.

Question Image
Identify the original shapes and describe all the transformations you can see in the design.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 11

This pattern is based on traditional Aztec print designs.

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Would you consider this a tessellation? Justify your response.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 12

This is an example of a fractal design. In math, a fractal is an abstract object formed by a never-ending pattern repeated at increasingly small scales.

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Describe the dilations that you see in the fractal design.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Practice 5>Q 12

This is an example of a fractal design. In math, a fractal is an abstract object formed by a never-ending pattern repeated at increasingly small scales.

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Could this shape be tessellated? Explain.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Unit review>Q 1

Copy and complete the table below:

Point	Translation up $3$ units	Translation left $5$ units	Translation down $2$ units and right $7$ units	Dilation by a scale factor of $4$ about the origin
$(0, 0)$
$(6, 1)$
$(3, - 2)$
$(- 4, 7)$
$(- 8, - 5)$

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 6 - Geometric Transformations Expressing Beliefs and Values>Unit review>Q 2

Plot the image of given shape on a Cartesian grid.

Translation $4$ units right and $4$ units down

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Graph the image of the triangle $A B C$ after a dilation with a scale factor of $\frac{1}{3}$ , centered at the origin.

Important Questions on Geometric Transformations Expressing Beliefs and Values

Learn and Prepare for any exam you want !

Graph the image of the triangle ABC after a dilation with a scale factor of 13, centered at the origin.

Important Questions on Geometric Transformations Expressing Beliefs and Values

Learn and Prepare for any exam you want !

Graph the image of the triangle $A B C$ after a dilation with a scale factor of $\frac{1}{3}$ , centered at the origin.