IsometriesRotations TranslationsCompositions

Isometries-100 homeanswer What is the definition of an isometry? Give three examples of isometries.

Isometries-100 Answer Isometry: a transformation that perseveres length, angle measure, parallel lines, etc. ex. Reflections Rotations Translations home question

Isometries-200 Which of the following is not a rotation of ? home answer a) b) c)

Isometries-200 Answer c) home question

Isometries-300 True or false? 1)Transformations that are not isometries are called rigid transformations. 2)Flips, turns and slides are nicknames for reflections, rotations and translations 3)Isometries preserve angle measures and parallel lines homeanswer

Isometries-300 Answer 1.False 2.True 3.True homequestion

Isometries-400 Find the value of each variable if the given transformation is an isometry home answer a° 50°b° 2c d 50°

Isometries-400 Answer a=90° c=2 2c+3=7 2c=4 c=2 b=40° d= d= d=3 40 homequestion

Isometries-500 Is the given transformation an isometry? ABC XYZ A=(-4,2) X=(2,2) B=(-1,4) Y=(4,-1) C=(-1,1) Z=(1,-1) home answer

Isometries-500 Answer Yes Use the distance formula to compare the side lengths AB=√(-4+1)²+(2-4)² BC=√(-1+1)²+(4-1)² AC=√(-4+1)²+(2-1)² =√(-3)²+(-2)² =√(0)²+(3)² =√(-3)²+(1)² =√9+4 =√9 =√9+1 =√13 =3 =√10 XY=√(2-4)²+(2+1)² YZ=√(4-1)²+(-1+1)² XZ=√(2-1)²+(2+1)² =√(-2)²+(3) ² =√(3)²+(0)² =√(1)²+(3)² =√4+9 =√9 =√1+9 =√13 =3 =√10 AB=XY BC=YZ AC=XZ home question

Rotations-100 homeanswer Does this figure have rotational symmetry? If so, describe the rotation that maps the figure onto itself.

Rotations-100 Answer Yes, the star does have rotational symmetry. To map the figure onto itself, you could rotate the object 72° or 144°. homequestion

Rotations-200 l A=(2,-3) A l =(-3,-2) If A was rotated clockwise around the origin, what was the angle of rotation? homeanswer

Rotations-200 Answer 90° In a 90° clockwise rotation, (x,y) (y,-x) If you use that information, you can substitute in (2,-3) to get (-2,-3), which are the coordinates of the given pre-image and image homequestion

Rotations-300 home answer 138°.A.A.Al.Al. A ll What is the measure of the angle of rotation? m K

Rotations-300 Answer 84 ° When you reflect a figure over line k then over line m, the angle of rotation is 2x (x=the measure of the acute angle formed by k and m) So, x= x=42 2(42)=84 ° home question

Rotations-400 Rotate (7,-2) 90°clockwise around the origin. Name the point of the image. Do the same for 180° and 270° clockwise. home answer

Rotations-400 Answer 90°=(-2, -7) because (x,y) (y,-x) 180°=(-7,2) because (x,y) (-x,-y) 270°=(2,7) because (x,y) (-y,x) homequestion

Rotations-500 home answer Find the values of all the variables 5 5c 10 2d+2 8 4b a° 65°

Rotations-500 Answer a=130°c=1 a=2(65) 5c=5 a=130 c=1 b=2d=4 4b=8 2d+2=10 b=2 2d=8 d=4 home question

Translations-100 Reflect AB, A=(3,-3) B= (2,-4), over y=1. What are the coordinates of A l and B l home answer

Translations-100 Answer A l =(3,5) B l =(2,-6) home question

Translation-200 Find the other endpoint using the following vectors. 1.(-4,0) vector 2. (5, -2) vector home answer

Translation-200 Answer homequestion 1.(-2,-3) (-4+2,0-3) (-2,-3) 2. (10,-1) (5+5,-2+1) (10,-1)

Translation-300 home answer Use the following coordinate notation to find the other endpoint. (x, y) (x+2, y-3) 1.(1,4) 2. (-3, -1)

Translation-300 Answer 1.(3,1) (1+2,4-3) (3,1) 2.(-1,-4) (-3+2,-1-3) (-1,-4) home question

Translation-400 A translation of AB is described by vector PQ. Find the value of each variable. A(w-5,-3)A l (10,x-1) B(z,3y+1)B l (5,5) home answer

Translation-400 Answer w=10y=3 w-5+2=10 3y+1-5=5 w-3=10 3y-4=5 w=13 3y=9 x=-7 y=3 -3-5=x-1z=3 -8=x-1 z+2=5 -7=x z=3 home question

Translation-500 Write the equation for the line of reflection A=(2,3) B=(6,-1) home answer

Translation-500 Answer y= x-3 Explanation: (2,3) (6,-1) Slope= (3+1)=-1 midpoint=( )= (4,1) (2-6) 2, 2 Perp. Line slope=1 y=1x+b 1=1(4)+b 1=4+b -3=b y=x-3 homequestion

Compositions-100 What is a composition? What is a glide reflection? home answer

Compositions-100 Answer A composition is when 2 or more transformations are combined to form a single transformation A glide reflection is a transformation in which every point P is mapped onto P ll by the following 2 steps -a translation that maps P onto P l -a reflection in line k such that the line of translation is parallel to reflection line k question home

Compositions-200 When you switch the order of transformations, does it affect the final image? In what cases? home answer

Compostitions-200 Answer In a composition, it does affect the final image, but it does not in a glide reflection. home question

Compostitions-300 Rotate A(3,2) 90° about the origin and reflect over the x-axis. homeanswer

Compositions-300 Answer A l (2,-3) A ll (2,3) home question

Compositions-400 Sketch the image of AB, A(4,2) B(7,0), after a composition using the given transformations (in the given order) Translation: (x,y) (x-4,y+2) Rotation: 270° clockwise about the origin home answer

Compositions-400 Answer Translation: A(0,4) B(3,2) Rotation: A(-4,0) B(-2,3) home question

Compositions-500 Sketch the image of A (-5,2) after translating it using vector and reflecting over x=4 home answer

Compositions-500 Answer After translation: A l (-2,-2) After reflection: A ll (10,-2) homequestion