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mathematics
holt mcdougal larson geometry
Holt McDougal Larson Geometry 1st Edition Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff - Solutions
Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Find the value of x. Q 15 P' R' 12 X P Q 8 R- C
Use the translation (x, y) → (x-8, y + 4).What is the image of A(2, 6)?
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 x = 3 (x, y) → (x, y + 4)
Use the diagram to write a matrix to represent the given polygon.Quadrilateral BCDE A E 2 y B D C X
Add, subtract, or multiply. 2.6]-[- 4 -2 2.6 [0.8 69 -1 3
Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. 눈
Use the translation (x, y) → (x - 8, y + 4).What is the image of B(-1, 5)?
Describe and correct the error in finding the scale factor k of the dilation. 3 12 id k = || 6/blo = 4 x
Use the translation (x, y) → (x - 8, y + 4).What is the preimage of C'(-3, -10)?
Use the diagram to write a matrix to represent the given polygon. Pentagon ABCDE
Match the diagram with the angle of rotation.
Graph the reflection of the polygon in the given line. x = -1 A B -2 C 1 АУ AX
Add, subtract, or multiply. ][] 7 -3 2 5 1-4 3
Copy the diagram. Then draw the given dilation.Center H; k = 2 D G HO E F ¡
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 = x (x, y) → (x + 2, y + 2)
Match the diagram with the angle of rotation.
Graph the image of the polygon after the reflection in the given line. x-axis y A B C D X
Match the diagram with the angle of rotation.
Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.
Graph the reflection of the polygon in the given line. y-axis C 1 Ay A 1 в X
Graph the image of the polygon after the reflection in the given line. y = 3 A B 1 y D C X
Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. Δ
The vertices of ΔPQR are P(2, 4), Q(6, 0), and R(7, 2). Graph the image of ΔPQR after a composition of the transformations in the order they are listed. Translation: Rotation: 90° about the origin (x, y) → (x-3, y + 2) -
Use the translation (x, y) → (x - 8, y + 4).What is the preimage of D'(4, -3)?
Graph the reflection of the polygon in the given line. y = -3 Ay C D A B X
Copy the diagram. Then draw the given dilation.Center J; k = 2 D G H. E F J
The vertices of ΔPQR are P(-2, 3), Q(1, 2), and R(3, -1). Graph the image of the triangle using prime notation. (x, y) (x + 9, y − 2) →
Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.
Trace the polygon and point P on paper. Then draw a rotation of the polygon the given number of degrees about P. 30° •Р А B C
Graph the image of the polygon after the reflection in the given line. y = -x B A 2 C y 1 x
The vertices of ΔPQR are P(2, 4), Q(6, 0), and R(7, 2). Graph the image of ΔPQR after a composition of the transformations in the order they are listed. Translation: Translation: (x, y) → (x + 12, y + 4) (x,y) → (x-5, y- 9)
The vertices of ΔPQR are P(-2, 3), Q(1, 2), and R(3, -1). Graph the image of the triangle using prime notation. (x, y) → (x-2, y - 5) -
Graph the reflection of the polygon in the given line. y = x y 1 B C A X
Determine whether the figure has line symmetry and whether it has rotational symmetry. Identify all lines of symmetry and angles of rotation that map the figure onto itself.
Copy the diagram. Then draw the given dilation.Center F; k = 2 D G H. E F J
Trace the polygon and point P on paper. Then draw a rotation of the polygon the given number of degrees about P. 150° F P G
The vertices of ΔPQR are P(-2, 3), Q(1, 2), and R(3, -1). Graph the image of the triangle using prime notation. (x, y) (x1, y + 3)
Find the image matrix that represents the rotation of the polygon. Then graph the polygon and its image. AABC: 246 25 1 ; 90° rotation
Determine whether the figure has line symmetry and whether it has rotational symmetry. Identify all lines of symmetry and angles of rotation that map the figure onto itself.
Graph the reflection of the polygon in the given line. y=-x D A C 1 У В 2 х
Copy the diagram. Then draw the given dilation. Center J; k= 11/123
The vertices of ΔPQR are P(2, 4), Q(6, 0), and R(7, 2). Graph the image of ΔPQR after a composition of the transformations in the order they are listed. Reflection: in the x-axis Rotation: 90° about the origin
Trace the polygon and point P on paper. Then draw a rotation of the polygon the given number of degrees about P. 130° Q R T P S
Graph the reflection of the polygon in the given line. y = x B 1 y 1 A C D
Find the image matrix that represents the rotation of the polygon. Then graph the polygon and its image. KLMN: -5 -2 -3 -5 0 3 -1 -3 ; 180° rotation
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' Ay C' A B C X
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(-5, 2), G(-2, 4) Translation: (x, y) Reflection: in the x-axis (x + 3, y - 8)
Determine whether the figure has line symmetry and whether it has rotational symmetry. Identify all lines of symmetry and angles of rotation that map the figure onto itself. FRASI
The diagonals of rhombus WXYZ intersect at V. Given that m∠XYW = 62°, find the indicated measure. ~ m/WXY = ?
The coordinates of ΔPQR are P(3,1), Q(3,3), and R(6,1). Graph the image of the triangle after the translation. (x, y) → (x + 3, y)
Quadrilateral EFGH is a kite. Find m∠G. E 55° ++ 100% H G
The diagonals of rhombus WXYZ intersect at V. Given that m∠XYW = 62°, find the indicated measure. 서 m∠XVY= ?
The coordinates of ΔPQR are P(3,1), Q(3,3), and R(6,1). Graph the image of the triangle after the translation. (x, y) → (x-3, y)
The coordinates of ΔPQR are P(3,1), Q(3,3), and R(6,1). Graph the image of the triangle after the translation. (x, y) → (x, y + 2)
Quadrilateral EFGH is a kite. Find m∠G. F G 80° E H
Find the sum, difference, product, or quotient. -16 - 7
The coordinates of ΔPQR are P(3,1), Q(3,3), and R(6,1). Graph the image of the triangle after the translation. (x, y) → (x + 3, y + 2)
Find the sum, difference, product, or quotient. 6 + (-12)
Find the sum, difference, product, or quotient. (13) (-2)
Find the sum, difference, product, or quotient. 16 ÷ (-4)
Determine whether the two triangles are similar. If they are, write a similarity statement. S Q P R T
Find the unknown side length. Write your answer in simplest radical form. 26 31
Quadrilateral EFGH is a kite. Find m∠G. E H
In the diagram, DC is the perpendicular bisector of AB.Find BD. A 30 10x - 6 C 4x D 7x + 2 B
The diagonals of rhombus WXYZ intersect at V. Given that m∠XYW = 62°, find the indicated measure. m/ZYW = ?
Write a matrix to represent the given polygon.Triangle B in Exercise 40 1 Ау 1 ДА B A Х
Spirals have a type of symmetry called spiral, or helical, symmetry. Describe the two transformations involved in a spiral staircase. Then explain the difference in transformations between the two staircases at the right.
You are snowshoeing in the mountains. The distances in the diagram are in miles. Write the component form of the vector.From the hotel back to your cabin N W E S Ski lodge (1,2) Cabin (0, 0) Hotel (4,2) X
Two art classes are buying supplies. A brush is $4 and a paint set is $10. Each class has only $225 to spend. Use matrix multiplication to find the maximum number of brushes Class A can buy and the maximum number of paint sets Class B can buy. Explain. Class A x brushes 12 paint sets Class B 18
Use the graph of y = 2x - 3.a. Rotate the line 90°, 180°, 270°, and 360° about the origin. Describe the relationship between the equation of the preimage and each image. b. Do you think that the relationships you described in part (a) are true for any line? Explain your reasoning. y 2 X
Use the graph of the quadratic equation y = x2 + 1 at the right.a. Rotate the parabola by replacing y with x and x with y in the original equation, then graph this new equation. b. What is the angle of rotation? c. Are the image and the preimage both functions? Explain. درا 3 y سیار
Prove the Reflection in Parallel Lines Theorem. J' KK' td- H m K"
By adjusting the distance between the negative and the enlarged print in a photographic enlarger, you can make prints of different sizes. In the diagram shown, you want the enlarged print to be 9 inches wide (A'B'). The negative is 1.5 inches wide (AB), and the distance between the light source and
The total United States production of corn was 8,967 million bushels in 2002, and 10,114 million bushels in 2003. The table shows the percents of the total grown by four states.a. Use matrix multiplication to find the number of bushels (in millions) harvested in each state each year. b. How many
A painter sketches plans for a mural. The plans are 2 feet by 4 feet. The actual mural will be 25 feet by 50 feet. What is the scale factor? Is this a dilation? Explain.
Copy the figure and draw its image after the reflection.Reflect the figure in the x-axis. y X
Copy the figure and draw its image after the reflection.Reflect the figure in the y-axis. y X
Graph a polygon in a coordinate plane. Draw a figure that is similar but not congruent to the polygon. What is the scale factor of the dilation you drew? What is the center of the dilation?
Write a matrix to represent the given polygon.Triangle A in Exercise 40 -1 y A A B X
In the diagram, DC is the perpendicular bisector of AB.What is the value of x? A 30 10x - 6 c1 4x D 7x + 2 B
Find the unknown side length. Write your answer in simplest radical form. 8 12
A point in space has three coordinates (x, y, z). From the origin, a point can be forward or back on the x-axis, left or right on the y-axis, and up or down on the z-axis. The endpoints of segment AB in space are A(2, 0, 0) and B(2, 3, 0), as shown at the right.a. Rotate AB 90° about the x-axis
You are studying an amoeba through a microscope. Suppose the amoeba moves on a grid-indexed microscope slide in a straight line from square B3 to square G7.a. Describe the translation. b. Each grid square is 2 millimeters on a side. How far does the amoeba travel? c. Suppose the amoeba moves from
A polar coordinate system locates a point in a plane by its distance from the origin O and by the measure of an angle with its vertex at the origin. For example, the point A(2, 30°) at the right is 2 units from the origin and m∠XOA = 30°. What are the polar coordinates of the image of point A
Find the unknown side length. Write your answer in simplest radical form. 16 30
In the diagram, DC is the perpendicular bisector of AB.What segment lengths are equal? A 30 10x - 6 CA 4x D 7x + 2 B
Use the diagram to prove that you can see your full self in a mirror that is only half of your height. Assume that you and the mirror are both perpendicular to the floor.a. Think of a light ray starting at your foot and reflected in a mirror. Where does it have to hit the mirror in order to reflect
You have an 8 inch by 10 inch photo.a. What is the area of the photo? b. You photocopy the photo at 50%. What are the dimensions of the image? What is the area of the image? c. How many images of this size would you need to cover the original photo?
Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain your reasoning. 78° 78°
Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain your reasoning. 8 6 8 6
Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain your reasoning. 呢 10, 10
Determine whether the two triangles are similar. If they are, write a similarity statement. B A 15 20 C 12 9 E D
Points A, B, C, and D are the vertices of a quadrilateral. Give the most specific name for ABCD. Justify your answer. A(3, 0), B(7, 2), C(3, 4), D(1, 2)
Points A, B, C, and D are the vertices of a quadrilateral. Give the most specific name for ABCD. Justify your answer. A(2, 0), B(7, 0), C(4, 4), D (2, 4)
The outline of the playing field at a baseball park is a polygon, as shown. Find the sum of the measures of the interior angles of the polygon.
In Exercises 29-31, determine whether there is enough information to prove that JKLM is an isosceles trapezoid. Explain. GIVENJKLM, ZJKL = 2KJM M L K
In the diagram, ABCD is a parallelogram, BF = DE = 12, and CF = 8. Find AE. Explain your reasoning. D E F C B
The floor of the greenhouse shown is a shaped like a regular decagon. Find the measure of an interior angle of the regular decagon. Then find the measure of an exterior angle.
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. mL DAC
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