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mathematics
holt mcdougal larson geometry

Questions and Answers of Holt McDougal Larson Geometry

Write a plan for proof for one case of the Composition Theorem. Q Q'e R' R P R" m Q"
The Castillo de San Marcos in St. Augustine, Florida, has the shape shown.a. What kind (s) of symmetry does the shape of the building show? b. Imagine the building on a three-dimensional coordinate
You are snowshoeing in the mountains. The distances in the diagram are in miles. Write the component form of the vector.From the ski lodge to the hotel N W E S Ski lodge (1, 2) Cabin (0,
Use the point P(-3, 6). Find the component form of the vector that describes the translation to P'. P'(-2, 0)
What is the value of y in the rotation of the triangle about P? Зу X 120° P 5 сл 10 x+7
Find point C on the x-axis so AC + BC is a minimum. A(4, -3), B(12,-5)
Think of each translation as a vector. Describe the vertical component of the vector. Explain.
Find the image matrix that represents a dilation of the polygon centered at the origin with the given scale factor. Then graph the polygon and its image. J L M -6 -3 3 0 3 N 3 30-3 ; k 2/3
Use the point P(-3, 6). Find the component form of the vector that describes the translation to P'. P'(-3,-5)
In Exercises 17-20, use the description to draw a figure. If not possible, write not possible.A trapezoid with rotational symmetry.
Find point C on the x-axis so AC + BC is a minimum. A(-8, 4), B(-1, 3)
Think of each translation as a vector. Describe the vertical component of the vector. Explain.
Draw a polygon with 180° rotational symmetry and with exactly two lines of symmetry.
Which product is not defined? A 1 3 12 6 15 9 [[30] B [320] C 15 6 -3 4 0 D [39] [55]
How many lines of symmetry does a circle have? How many angles of rotational symmetry does a circle have? Explain.
How many planes of symmetry does a cube have?
Copy the diagram. Then draw the given dilation. Center F; k = 22
What is the line of reflection for ΔABC and its image? C A C' 2 y B B' 2 A'
Rotate the figure the given number of degrees about the origin. List the coordinates of the vertices of the image. 90° A 1 y 1 B C X
Identify the line symmetry and rotational symmetry of the figure at the right. х
ΔA'B'C' is the image of ΔABC after a translation. Write a rule for the translation. Then verify that the translation is an isometry. A B A' B' C y 1 C' X
Copy the diagram. Then draw the given dilation. Center D; k= N/W 2
Graph F"G" after a composition of the transformations in the order they are listed. Then perform the transformations in reverse order. Does the order affect the final image F"G"? F(-1, -8), G(-6,
Which statement best describes the rotational symmetry of a square?
Draw a figure that has one line of symmetry and does not have rotational symmetry. Can a figure have two lines of symmetry and no rotational symmetry?
Find the image matrix that represents the translation of the polygon. Then graph the polygon and its image. A B -2 2 4 C 1 : 4 units up 1-3
Describe and correct the error in graphing the translation of quadrilateral EFGH. (x, y) → (x1, y — 2) Ay 1 E E H H' F LL G F' ட்ட AX x
Rotate the figure the given number of degrees about the origin. List the coordinates of the vertices of the image. 180° 1 y J 1 M K L X
Copy the diagram. Then draw the given dilation. = 1/1/2 Center G; k =
Describe the composition of transformations. A C B" Ay 2 B C" A" A' C' 1 B' X
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect A A B C -2 3 4 a 5 -3 6 in the x-axis.
Write a matrix for the polygon. Then find the image matrix that represents the polygon after a reflection in the given line. x-axis A -2- D y 1 C B X
Rotate the figure the given number of degrees about the origin. List the coordinates of the vertices of the image. 270° Q R S -1 1 T y
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect P 2 [- -2 Q R 6 5 -8 -3 S 2 -5 ] in the y-axis.
Find the image matrix that represents the translation of the polygon. Then graph the polygon and its image. F G H 2 58 2 3 1 3 1 J 5 -1 2 units left and 3 units down
Determine whether the flag has line symmetry and/or rotational symmetry. Identify all lines of symmetry and/or angles of rotation that map the figure onto itself.
Describe the composition of transformations. C" B" B' C' D" D' y 2 A" A' A 2 D B C X
Find the image matrix that represents the translation of the polygon. Then graph the polygon and its image. L M N P 202 -1 3 3 3; 4 units right and -1 2 units up
Describe and correct the error made in describing the symmetry of the figure. x The figure has 1 line of symmetry and 180° rotational symmetry.
Simplify the product. ¹ [³ 4 3 7 09 4 -1
Find the image matrix that represents the rotation of the polygon about the origin. Then graph the polygon and its image. A B C 154 4 6 3 ; 90°
Determine whether the flag has line symmetry and/or rotational symmetry. Identify all lines of symmetry and/or angles of rotation that map the figure onto itself.
Write a matrix for the polygon. Then find the image matrix that represents the polygon after a reflection in the given line. y-axis 1 y A 1 C B X
In the diagram, k ∣∣ m, ΔABC is reflected in line k, and ΔA'B'C' is reflected in line m.A translation maps ΔABC onto which triangle? A B CC' B' A' m A" B" C"
Name the vector and write its component form. C D
Find the image matrix that represents the rotation of the polygon about the origin. Then graph the polygon and its image. J K 1 2 1 -1 L 0 -3 ; 180°
Describe and correct the error made in describing the symmetry of the figure. x The figure has 1 line of symmetry and 180° rotational symmetry.
Simplify the product. -5 -2 -5 7 1 3 4 0 -1
Determine whether the flag has line symmetry and/or rotational symmetry. Identify all lines of symmetry and/or angles of rotation that map the figure onto itself.
Name the vector and write its component form. T R
Write a matrix for the polygon. Then find the image matrix that represents the polygon after a reflection in the given line. y-axis A 1 Ay 1 C B X
Name the vector and write its component form. AP J
Simplify the product. 9 이우 0 3 -1 7 2 0
Find the image matrix that represents the rotation of the polygon about the origin. Then graph the polygon and its image. P Q R S -4 2 2-4 -4 -2 -5 -7 ; 270°
Describe and correct the error in finding the image matrix of ΔPQR reflected in the y-axis. 1 * * ]X ][ 0 -5 4 48 -2 2²] - [= -1 -5 -4 4-2 -8 -1
Find the image matrix that represents a dilation of the polygon centered at the origin with the given scale factor. Then graph the polygon and its image. DEF 235 164 ; k = 2
Use the point P(-3, 6). Find the component form of the vector that describes the translation to P'. P'(0, 1)
The endpoints of AB are A(-1, 1) and B(2, 3). Describe and correct the error in setting up the matrix multiplication for a 270° rotation about the origin. 270° rotation of AB -1 2 RX 1 3 1
Use the point P(-3, 6). Find the component form of the vector that describes the translation to P'. P'(-4, 8)
In Exercises 17-20, use the description to draw a figure. If not possible, write not possible.A quadrilateral with no line of symmetry.
Find point C on the x-axis so AC + BC is a minimum. A(1, 4), B(6, 1)
In the diagram, k ∣∣ m, ΔABC is reflected in line k, and ΔA'B'C' is reflected in line m. Is the distance from B' to m the same as the distance from B" to m? Explain.
Find the image matrix that represents a dilation of the polygon centered at the origin with the given scale factor. Then graph the polygon and its image. GH J -20 6 -2] ; * = k -4 2-2 2
The endpoints of AB are A(-1, 1) and B(2, 3). Describe and correct the error in setting up the matrix multiplication for a 270° rotation about the origin. 270° rotation of AB -1 2 0 1 MAX 1 3
In Exercises 17-20, use the description to draw a figure. If not possible, write not possible.An octagon with exactly two lines of symmetry.
In Exercises 17-20, use the description to draw a figure. If not possible, write not possible.A hexagon with no point symmetry.
Give the most specific name for the quadrilateral. Explain your reasoning. A D C 53° в
Give the most specific name for the quadrilateral. Explain your reasoning. J 1 K 7 10 M L
Write a rule for the translation of ΔABC to ΔA'B'C'. Then verify that the translation is an isometry. 1 y A 1 B C A' B' C' X
What is a center of symmetry?
What is a scalar?
What is a center of rotation?
To find the sum of two matrices, add corresponding _?_.
Write a rule for the translation of ΔABC to ΔA'B'C'. Then verify that the translation is an isometry. A' B' y C' B 1 A X C
What is a line of reflection?
A __?__ is a quantity that has both__?__ and magnitude.
In a glide reflection, the direction of the translation must be __?___ to the line of reflection.
How can you determine whether two matrices can be added? How can you determine whether two matrices can be multiplied?
Compare the coordinate rules and the rotation matrices for a rotation of 90°.
If you know the scale factor, explain how to determine if an image is larger or smaller than the preimage.
Explain how to find the distance from a point to its image if you know the distance from the point to the line of reflection.
Describe the difference between a vector and a ray.
Copy the diagram. Then draw the given dilation.Center H; k = 3 D G H. E F ;
Use the diagram to write a matrix to represent the given polygon. ΔΕΒΕ
How many lines of symmetry does the triangle have?
Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Find the value of x. C 6 -14- P X 'P'
Identify the type of transformation, translation, reflection, or rotation, in the photo. Explain your reasoning.
The endpoints of CD are C(2,-5) and D(4, 0). Graph the image of CD after the glide reflection. Translation: Reflection: in the y-axis (x, y) → (x, y − 1) -
Write a rule for the translation of ΔABC to ΔA'B'C'. Then verify that the translation is an isometry. B' A' B A 1 y 1 C'C A4
Graph the reflection of the polygon in the given line. x-axis Ay 1 A B C X
Identify the type of transformation, translation, reflection, or rotation, in the photo. Explain your reasoning.
Use the diagram to write a matrix to represent the given polygon. ΔΕCD
Graph the reflection of the polygon in the given line. y-axis A 3 B نیا y 1 D C X
Explain why a glide reflection is an isometry.
How many lines of symmetry does the triangle have?
Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Find the value of x. P 9 -15- P' x C
Add, subtract, or multiply. 3-8 9 4.3 + -10 2 5.1 -5
How many lines of symmetry does the triangle have?
The endpoints of CD are C(2,-5) and D(4, 0). Graph the image of CD after the glide reflection. Translation: Reflection: in y = -1 (x, y) → (x-3, y)
Graph the reflection of the polygon in the given line. y = 2 D A C 1 y B 1 x

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