Geometry Final Ch 12

Find the coordinates of the image when each point is reflected across the given line (3,1); y = x + 2

(-1,5) Pg 830 #51

Use arrow notation to describe the mapping of each point when it is reflected across the given line. (0,-5); y = x

(0,-5) -> (-5,0) Pg 828 #35

Use arrow notation to describe the mapping of each point when it is reflected across the given line. (0,12); x-axis

(0,12) -> (0,-12) Pg 828 #33

Find the coordinates of the image when each point is reflected across the given line (4,2); y = 3

(4,4) Pg 830 #49

Use arrow notation to describe the mapping of each point when it is reflected across the given line. (5,2); x-axis

(5,2) -> (5,-2) Pg 828 #31

An artist uses a coordinate plane to plan the motion of an animated car. To simulate the car driving around a curve, the artist places the car at the point (10,0) an then rotates it about the origin by 30*. Give the car's final position, rounding the coordinates to the nearest tenth.

(8.7,5) Pg 842 #11

What is the image of P(1,3) when it is translated along the vector {-3,5}? A) (-2,8) B) (0,6) C) (1,3) D) (0,4)

A Pg 836 #39

^ABC is reflected across the y-axis. Then its image is rotated 90* about the origin. What are the coordinates of the final image of point A under this composition of transformations? A) (-1,-2) B) (-2,1) C) (1,2) D) (-2,-1)

A Pg 853 #23

Sketch the image of pentagon ABCDE under a rotation of 180* about the origin Give the vertices of the image.

A'(-2,3), B'(-3,0), C'(0,-3), D'(3,0), E'(2,3) Pg 844 #39

Which vector translates point Q to point P? A) {-2,-4} B) {4,-2} C) {-2,4} D) {2,-4}

C Pg 837 #41

Which is equivalent to the composition of two translations? A) Reflection B) Rotation C) Translation D) Glide reflection

C Pg 853 #25

Explain the steps you would use to draw a glide reflection.

Draw a figure and translate it along a vector. Then reflect the image across a line. Pg 851 #1

The six cars of a Ferris wheel are located at the vertices of a regular hexagon. Which rotation about point P maps car A to car C? F) 60* G) 90* H) 120* J) 135*

H Pg 845 #43

Tell whether each transformation appears to be a translation.

No Pg 834 #1

Tell whether each transformation appears to be a translation.

No Pg 834 #13

Tell whether each transformation appears to be a rotation.

No Pg 842 #3

Tell whether each transformation appears to be a rotation.

No Pg 842 #15

A student wrote the following in his math journal. "Under a rotation, every point moves around the center of rotation by the same angle measure. This means that every point moves the same distance." Do you agree? Explain

No; although all points are rotated around the center of rotation by the same angle, points farther from the center of rotation move a greater distance than pts that are closer to the center of rotation. Pg 844 #37

The points of a plane are translated along the given vector AB. DO any points remain fixed under this translation? That is, are there any points from which the image coincides with the preimage? Explain

No; there are no fixed points because by definition of a translation every point must move by the same distance Pg 836 #27

Reflect the figure with the given vertices across the given line. M(2,1), N(3,1), P(2,-1), Q(1,-1); y = x

Pg 827 #11

Copy each figure and the line of refection. Draw the reflection of the figure across the line.

Pg 827 #7

Reflect the figure with the given vertices across the given line. A(-2,1), B(2,3), C(5,2); x-axis

Pg 827 #9

Copy each figure and the line of refection. Draw the reflection of the figure across the line.

Pg 828 #17

Cara is playing pool. She wants to hit the ball at point A without hitting the ball at point B. She has to bounce the cue ball, located at point C, off the side rail and into her ball. Draw the diagram that shows the exact point along the rail that Cara should aim for.

Pg 828 #19

Reflect the figure with the given vertices across the given line. M(-4,-1), N(-1,-1), P(-2,-2); y = x

Pg 828 #21

Reflect the figure with the given vertices across the given line. S(-1,1), T(1,4), U(3,2), V(1,-3); y = x

Pg 828 #23

Copy each figure and the line of refection. Draw the reflection of the figure across the line.

Pg 828 #25

In chemistry, chiral molecules are mirror images of each other. Although they have similar structures, chiral molecules can have very different properties. For example, the compound (-(+)-limonene smalls like oranges, while its mirror image, S-(-)-limonene smells like lemons. Use the figure and the given line to draw S-(-)-limonene.

Pg 828 #27

Each figure shows a preimage and image under a reflection. Copy the figure and draw the line of reflection.

Pg 828 #29

Draw the reflection of the figure across the y-axis.

Pg 829 #41

In the reflection shown, the shaded figure is the preimage. Which of these represents the mapping? F) MJNP -> DSWG G) DGWS ->MJNP H) JMPN -> GWSD J) PMJN -> SDGW

Pg 830 #47

Copy each figure and the translation vector. Draw the translation of the figure along the given vector.

Pg 834 #5

Translate the figure with the given vertices along the given vector. A(-4,-4), B(-2,-3), C(-1,3);(5,0)

Pg 834 #7

Translate the figure with the given vertices along the given vector. J(-2,2), K(-1,2), L(-1,-2), M(-3,-1);(3,2)

Pg 834 #9

Copy each figure and the translation vector. Draw the translation of the figure along the given vector.

Pg 835 #15

Translate the figure with the given vertices along the given vector. P(-1,2), Q(1,-1), R(3,1), S(2,3); (-3,0)

Pg 835 #17

Translate the figure with the given vertices along the given vector. D(0,15), E(-10,5), F(10,-5); (5,-20)

Pg 835 #19

Draw the translation of the graph of each function along the given vector. (3,0)

Pg 835 #21

Each figure shows a preimage (blue) and its image (red) under a translation. Copy the figure and draw the vector along which the polygon is translated.

Pg 836 #25

Copy each figure and the angle of rotation. Draw the rotation of the figure about point P by m(Angle)A.

Pg 842 #5

Rotate the figure with the given vertices about the origin using the given angle of rotation. A(1,0), B(3,2), C(5,0); 90*

Pg 842 #7

Rotate the figure with the given vertices about the origin using the given angle of rotation. D(2,3), E(-1,2), F(2,1); 180*

Pg 842 #9

Copy each figure and the angle of rotation. Draw the rotation of the figure about point P by m(Angle)A.

Pg 843 #17

Rotate the figure with the given vertices about the origin using the given angle of rotation. A(-1,0), B(-1,-3), C(1,-3), D(1,0); 90*

Pg 843 #19

Rotate the figure with the given vertices about the origin using the given angle of rotation. L(2,0), M(-1,-2), N(2,-2); 180*

Pg 843 #21

Copy each figure. Then draw the rotation of the figure about the red point using the given angle measure. 90*

Pg 843 #23

Copy each figure. Then draw the rotation of the figure about the red point using the given angle measure. 180*

Pg 843 #25

Rectangle RSTU is the image of rectangle LMNP under a 180* rotation about point A. Name each of the following: the image of point N

Pg 843 #27

Rectangle RSTU is the image of rectangle LMNP under a 180* rotation about point A. Name each of the following: the image of Line MN

Pg 843 #29

Each figure shows a preimage and its image under a rotation. Copy the figure and locate the center of rotation.

Pg 844 #33

Draw the result of the composition of isometries. Reflect rectangle PQRS across line m and then translate it along vector v.

Pg 851 #3

Copy each figure and draw two lines of reflection that produce an equivalent transformation. rotation with center P: ^ABC -> ^A'B'C'

Pg 851 #7

Draw the result of the composition of isometries. Rotate ^ABC 90* about point P and then reflect it across line l

Pg 851 #9

Copy each figure and draw two lines of reflection that produce an equivalent transformation. rotation with center Q: ^JKL -> ^J'K'L'

Pg 852 #13

Equilateral ^ABC is reflected across line AB. Then its image is translated along vector BC. Copy ^ABC and draw its final image

Pg 852 #15

If a transformation is an isometry how would you describe the relationship between the preimage and the image?

They are =~ (congruent) Pg 827 #1

Tell whether each transformation appears to be a translation.

Yes Pg 834 #11

Tell whether each transformation appears to be a translation.

Yes Pg 834 #3

Tell whether each transformation appears to be a rotation.

Yes Pg 842 #1

Tell whether each transformation appears to be a rotation.

Yes Pg 842 #13

To create the opening graphics for a televised football game, an animator reflects a picture of a football helmet across line l. She then reflects its image across line m, which intersects line l at a 50* angle. Describe a single transformation that moves the helmet from its starting position to its final position.

a rotation of 100* about the point of intersection of the lines Pg 851 #5

The point P(3,2) is translated along one of the following four vectors chosen at random: (-3,0), (-1,-4), (3,-2), and (2,3). Find the probability of each of the following. a. The image of P is in the fourth quadrant. b. The image of P is on an axis. C. The image of P is at the origin.

a. 1/4 b. 1/2 c. 0 Pg 835 #23

A miniature golf course includes a hole with a windmill. Players must hit the ball through the opening at the base of the windmill while the blades rotate. a. The blades take 20 seconds to make a complete rotation. Through what angle do the blades rotate in 4 seconds? b. Find the coordinates of point A after 4 seconds. (Hint: (4,3) is the center of rotation.)

a. 72* b. (4.9,5.9) Pg 843 #31

The photograph was made by placing a camera on a tripod and keeping the camera's shutter open for a long time. Because of Earth's rotation, the stars appear to rotate around Polaris, also known as the North Star. a. Estimate the angle of rotation of the stars in the photo. b. Use your result from part a to estimate the length of time that the camera's shutter was open (Hint: If the shutter was open for 24 hours, the stars would appear to make one complete rotation around Polaris.)

a. 90* b. 6 hours Pg 844 #35

In chess, a knight moves in the shape of the letter L. The pieces moves two spaces horizontally or vertically. Then it turns 90* in either direction and moves one more space. a. Describe a knight's move as a composition of transformations. b. Copy the chessboard with the knight. Label all the positions the knight can reach in one move. c. Label all the positions the knight can reach in two moves.

a. The move is a horizontal or vertical translation by 2 spaces followed by a vertical or horizontal translation by 1 space. Pg 852 #11

The figure shows one hole of a miniature golf course. a. Is it possible to hit the ball in a straight line from the tee T to the hole H? b. Find the coordinates of H', the reflection of H across Segment BC c. The point at which a player should aim in order to make a hole in one is the intersection of Segment TH' and BC. What are the coordinates of this point?

a. no b. (7,4) c. (6,3.5) Pg 829 #37

A cube has edges of length 2 cm. Point P is translated along vectors u, v, and w as shown. a. Describe a single translation vector that maps point P to point Q. b. Find the magnitude of this vector to the nearest hundredth.

a. the vector PQ b. 3.46 cm Pg 837 #43

Tell whether each statement is sometimes, always, or never true. A rotation is equivalent to a composition of two reflections.

always Pg 852 #19

Tell whether each statement is sometimes, always, or never true. An isometry changes the size of a figure

never Pg 852 #17

Tell whether each transformation appears to be a reflection.

no Pg 827 #13

Tell whether each transformation appears to be a reflection.

no Pg 827 #3

Tell whether each transformation appears to be a reflection.

no Pg 827 #5

Under a reflection in the coordinate plane, the point (3.5) is mapped to the point (5,3). What is the line of reflection? Is this the only possible line of reflection? Explain.

y=x Pg 829 #39

Tell whether each transformation appears to be a reflection.

yes Pg 827 #15

Find the vector associated with each translation. Then use the arrow notation to describe the mapping of the preimage to the image. the translation that maps point C to the origin

{-3,1}, (3,-1) -> (0,0) Pg 836 #33

Find the vector associated with each translation. Then use the arrow notation to describe the mapping of the preimage to the image. the translation that maps point C to point D

{3,-2}, (3,-1) -> (0,-3) Pg 836 #31

Find the vector associated with each translation. Then use the arrow notation to describe the mapping of the preimage to the image. the translation that maps point A to point B

{4, 0}, (-3,2) -> (1,2) Pg 836 #29