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MTH 214 Week 3 Checkpoint

The purpose of the MyMathLab® Checkpoint is to assess your understanding of weekly learning objectives.

Prerequisite Assignment: MyMathLab® Study Plan for Weekly Checkpoint

Complete this week’s MyMathLab® Checkpoint.

1. Click the Quiz tab.
2. Click External Content Launch to access MyMathLab®.
3. Click Homework and Tests in MyMathLab® on the top left corner of the screen.
4. Click the Checkpoint for this week.

Note: You must earn at least 80% of the Mastery Points in the weekly MyMathLab® Study Plan before you may start the weekly Checkpoint.

Draw a reflecting line to show that the name HAVAHHAVAH can be its own image under a reflection.

Choose the correct answer below.

A.

The collection of letters Upper H Upper A Upper V Upper A Upper H is shown. A dashed horizontal line passes through the middle of the collection of letters.

HAVAH

B.

The collection of letters Upper H Upper A Upper V Upper A Upper H is shown. A dashed line rising from left to right passes through the middle of the collection of letters.

HAVAH

C.

The collection of letters Upper H Upper A Upper V Upper A Upper H is shown. A dashed vertical line appears to the right of the collection of letters.

HAVAH

D.

The collection of letters Upper H Upper A Upper V Upper A Upper H is shown. A dashed vertical line appears passing through the middle letter.

HAVAH

On the grid, identify a tessellation of the plane using the following figure.

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Determine whether the figure could be its own image under some motion. If so, which one?

A square is divided into four identical right triangles. The vertices of the square are pointing up, right, down, and left. The triangles in the top half of the square are blue. The bottom left side of the square coincides with a leg of a blue, right triangle with a vertical hypotenuse. The square is rotated 90 degrees clockwise about its bottom vertex, is now all blue and missing the triangles in its bottom left section. The square is again rotated 90 degrees clockwise about its bottom vertex and now a smaller white square is in the top right section of the larger square. The top side of the smaller square coincides with a horizontal leg of a blue right triangle.

Choose the correct answer below.

A.

Yes commaYes, the figure isis its own image after a 180 degrees rotationa 180° rotation through thethrough the center.center.

B.

Yes, the figure is its own image after a 90degrees° rotation through the center.

C.

No commaNo, the figure is notis not its own image after any motion.any motion. nothing nothing

Your answer is correct.D.

Yes, the figure is its own image after a reflection across a vertical linea reflection across a vertical line through the center.

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On dot paper, use the pentomino shown on the right, to make a tessellation of the plane. There may be more than one correct tessellation.

Using what you learned by creating your own tesselation, determine which tessellations below correctly use only the given pentomino.

A grid composed of 7 rows and 7 columns of same-sized squares contains a six-sided polygon composed of the bottommost 4 squares in the leftmost column and the bottommost square in the second column from the left.

A

A figure contains 16 six-sided polygons, all of which have the same shape. Assuming the entire figure is divided into same-sized squares with side length 1 and the bottom left space in the figure has coordinates (1, 1), two of the six-sided polygons are composed of 5 squares with positions as follows: (1, 5), (1, 4), (1, 3), (1, 2), (2, 2); (2, 3), (2, 4), (2, 5), (2, 6), (1, 6). The two polygons combine to form the shape of a rectangle with height 5 units and width 2 units. The remaining 14 six-sided polygons combine in pairs to form 7 additional rectangles with the same dimensions. Overall, there are two rows and four columns of these rectangles with no gaps between any of the polygons.

B

A figure contains 8 six-sided polygons, 8 squares, and 4 rectangles. Assuming the entire figure is divided into same-sized squares with side length 1 and the bottom left space in the figure has coordinates (1, 1), some of the polygons are composed of squares with positions as follows: square, (1, 6); six-sided polygon, (1, 5), (1, 4), (1, 3), (1, 2), (2, 2); rectangle, (2, 3), (2, 4), (2, 5); six-sided polygon, (2, 6), (3, 6), (3, 5), (3, 4), (3, 3); square, (3, 2). These polygons combine to form the shape of a rectangle with height 5 units and width 3 units. The remaining polygons combine in the same way to form 3 additional rectangles with the same dimensions. Overall, there are two rows and two columns of these rectangles with no gaps between any of the polygons.

C

A figure contains 8 six-sided polygons, all of which have the same shape. Assuming the entire figure is divided into same-sized squares with side length 1 and the bottom left space in the figure has coordinates (1, 1), each polygon is composed of 5 squares with positions as follows: (1, 8), (1, 7), (1, 6), (1, 5), (2, 5); (2, 9), (2, 8), (2, 7), (2, 6), (3, 6); (3, 10), (3, 9), (3, 8), (3, 7), (4, 7); (4, 11), (4, 10), (4, 9), (4, 8), (5, 8); (5, 7), (6, 7), (6, 6), (6, 5), (6, 4); (4, 6), (5, 6), (5, 5), (5, 4), (5, 3); (3,5), (4, 5), (4, 4), (4, 3), (4, 2); (2, 4), (3, 4), (3, 3), (3, 2), (3, 1). There are no gaps between any of the polygons.

Choose the true statement below.

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A cube will tessellate space but a sphere will not. List several other solids that will tessellate space and several that will not.

Which solids will tessellate space? Select all that apply.

A.

Triangular prism

Your answer is correct.B.

Right rectangular prism

Your answer is correct.C.

Cylinder

D.

Tetrahedron

Isaiah says that the bricks used in a classroom wall construction form a tessellation. How do you respond?

Choose the correct answer below.

A.

Isaiah is correct. The bricks used in a classroom wall are comparable to a rectangle tiling a plane.

Your answer is correct.B.

Isaiah is incorrect. A tessellation must involve the rotation of a shape. Since the bricks do not rotate, they do not form a tessellation.

What transformation would move lizardlizard A to lizardlizard B?

In a pattern of identical lizard shapes, four yellow lizards meet at the tips of their mouths pointing inward up, right, down, and left and four green lizards meet diagonally at the tip of their tails. The lizards are arranged so that the green lizards fit inside the spaces between the yellow lizards. Lizard Upper A is the bottom right yellow lizard. Lizard Upper B is the top left green lizard.

A

B

Choose the correct answer below.

glide dash reflectionglide-reflection

translationtranslation

Your answer is correct.

reflectionreflection

rotationrotation

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Explain why only three types of regular polygons tessellate the plane.

Choose the correct answer below.

A.

In order for a regular polygon to tessellate the plane, its angle bisectors must intersect at 90degrees° angles.

B.

In order for a regular polygon to tessellate the plane, its exterior angle measure must be a divisor of 360degrees°. Only three regular polygons have exterior angles that divide 360degrees°. Those polygons are the equilateral triangle, regular hexagon, and regular nonagon.

C.

In order for a regular polygon to tessellate the plane, its interior angle measure must be a divisor of 360degrees°. Only three regular polygons have interior angle measures that divide 360degrees° . Those polygons are the equilateral triangle, square, and regular hexagon.

In order for a regular polygon to tessellate the plane, its number of sides must divide 9. Therefore only the equilateral triangle, regular hexagon and regular nonagon can tessellate the plane.

Type the coordinates of the images Upper S primeS′, Upper R primeR′, and Upper T primeT′ for each of the following points under the translation defined by (x,y)right arrow→(xplus+77,yminus−44).

a) S(66,1212)

b) R(negative 8−8,negative 4−4)

c) T(rr,ss)

a) S(66,1212)right arrow→Upper S primeS′

left parenthesis 13 comma 8 right parenthesis(13,8) (Type an ordered pair.)

b) R(negative 8−8,negative 4−4)right arrow→Upper R primeR′

left parenthesis negative 1 comma negative 8 right parenthesis(−1,−8) (Type an ordered pair.)

c) T(rr,ss)right arrow→Upper T primeT′

left parenthesis r plus 7 comma s minus 4 right parenthesis(r+7,s−4) (Type an ordered pair.)

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List several figures other than rectangles that tessellate the plane using translations.

Select all that apply.

A.

A trapezoid has a vertical left side, a right side that rises from left to right, and two horizontal bases where the top base is longer than the bottom base.

B.

A regular hexagon

Your answer is correct.C.

A polygon resembles a four sided polygon with two vertical sides where a portion of its bottom side has been removed and attached to its top side.

Your answer is correct.D.

An isosceles right triangle.

E.

A four sided polygon has two horizontal sides of equal length and two sides that rise from left to right of equal length. No interior angles measure 90 degrees.

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Gloria drew two examples of figures in which one is the image of the other under reflection in the y-axis as well as under a half-turn with center A. In the second example, the image of the two upper circles under reflection in line j are the two lower circles. However, the lower circles are also the image of the upper circles under a half-turn about N. Therefore, Gloria claims that the image of every figure under reflection can also be obtained by rotation. How do you respond?

x

y

D’

D

C

C’

B’

B

E

E’

N

j

A

A coordinate system has a horizontal x-axis and a vertical y-axis. Above the x-axis, two quadrilaterals are shown. The first has labeled vertices as follows beginning with the top left and moving clockwise, where all coordinates are in terms of tick marks: D prime, (negative 9, 6); E prime, (negative 3, 7); B prime, negative 3, 3); C prime, (negative 9, 4). The second has labeled vertices as follows beginning with the top left and moving clockwise: E, (3, 7); D, (9, 6); C, (9, 4); B, (3, 3). A point labeled A lies 5 units above 0 on the y-axis. Below the x-axis four circles appear organized in two rows each containing two circles. All four circles have a radius of 2 units. The top left circle is centered at (negative 2, negative 4). The top right circle is centered at (2, negative 4). The bottom left circle is centered at (negative 2, negative 8). The bottom right circle is centered at (2, negative 8). The top left circle is tangent to the top right and bottom left circles. The bottom right circle is tangent to the top right and bottom left circles. The y-axis passes between the columns of circles and a line labeled j passes between the rows of circles. A point labeled N lies 6 units below 0 on the y-axis.

Choose the correct answer below.

A.

If the circles are changed to squares, the resulting figure would refute Gloria’s claim.

B.

Gloria is incorrect. The figures drawn have additional reflection symmetries. Figures that don’t have such lines of symmetry will not have a half-turn symmetry.

Gloria is incorrect. In the first figure, the trapezoid on the right cannot be transformed into the trapezoid on the left by a rotation.

D.

These figures show that Gloria is correct.

Explore the Transformations eManipulative and then solve the problem.

A green crescent opens to the right.

A red crescent opens upward.

Describe the transformation from the green picture to the red picture.

Rotation

Identity

Glide-Reflection

Reflection

Consider the translation left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 2 comma y minus 2 right parenthesis(x,y)→(x+2,y−2). For each figure, find the coordinates of the images of the labeled points.

a. For the circle with center at B, type the images of the 3 labeled points.

A(minus−2,44)right arrow→Upper A primeA′

left parenthesis 0 comma 2 right parenthesis(0,2)

(Type an ordered pair.)

B(minus−2,1)right arrow→Upper B primeB′

left parenthesis 0 comma negative 1 right parenthesis(0,−1)

(Type an ordered pair.)

C(minus−2,negative 2−2)right arrow→Upper C primeC′

left parenthesis 0 comma negative 4 right parenthesis(0,−4)

(Type an ordered pair.)

b. For quadrilateral DEFG, type the image of each vertex.

D(negative 4−4,minus−1)right arrow→Upper D primeD′

left parenthesis negative 2 comma negative 3 right parenthesis(−2,−3)

(Type an ordered pair.)

E(negative 3−3,66)right arrow→Upper E primeE′

left parenthesis negative 1 comma 4 right parenthesis(−1,4)

(Type an ordered pair.)

F(33,55)right arrow→Upper F primeF′

left parenthesis 5 comma 3 right parenthesis(5,3)

(Type an ordered pair.)

G(1,minus−1)right arrow→Upper G primeG′

left parenthesis 3 comma negative 3 right parenthesis(3,−3)

(Type an ordered pair.)