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WorksheetsTopic 7: Rigid Transformations Practice
Total questions: 135
Worksheet time: 7hrs 4mins
What directions would you give?
Reflect over the line: ________
What changes when an ordered pair, or point, is reflected across the y-axis?
Neither the x-value nor the y-value
y-value only
x-value only
Both the x-value and the y-value
What is the rule for the reflection over the line y=x?
ry=x(x, y) → (–y, –x)
ry=–x(x, y) → (–y, –x)
ry=x(x, y) → (y, x)
ry=–x(x, y) → (y, x)
Identify the transformation from ABC to A'B'C'.
90o counterclockwise rotation
Reflection across the x-axis
Translation
90o clockwise rotation
(x, y) ----> (-x, y)
The point (-2,5) is reflected over the line x = 1. Find its image.
(4, 5)
( -2 , -5)
(2 , 5)
(2 , -5)
What is the rule for the following reflection?
Reflection across x-axis
Reflection across y-axis
Reflection across y = x
Reflection across y = −x
(x, y) ----> (x + 2, y - 3)
What vector translates triangle ABC to A’B’C’?
<-5, 1>
<5, -1>
<-6, 2>
<6, -2>
The image of point (2, 8) when translated using the rule (x, y) → (x, y-1) is:
(2, 7)
(1, 8)
(1, 7)
(0, 7)
What are the coordinates of R', the image of R(-1, 4), after a translation of 2 units right and 3 units down?
(-3, 1)
(3, 7)
(-1, 7)
(1, 1)
When a shape is translated in the coordinate plane, it has undergone a rigid transformation. Which of the following are definitely true statements about the image of a shape after a translation? Select all that apply.
The size of the shape is the same.
The orientation of the shape is the same.
A translation is in simple terms a flip.
Each point moves the same distance in the same direction.
Translate the blue shape to the pink shape...
5 Right
2 Down
5 Left
2 Up
3 Right
1 Down
3 Left
1 Up
Translate shape B to shape A...
5 Right
3 Up
5 Left
3 Down
3 Right
3 Up
3 Left
3 Down
Slide 3 up and 2 right
(x, y) -----> (x, y +4)
Determine how to translate triangle ABC to triangle A'B'C' ?
(x + 2, y - 5)
(x + 2, y - 9)
(x - 2, y - 9)
(x - 2, y + 9)
What is the algebraic representation of a figure is Translated 9 units right and 3 units down?
(x, y) -->
(x - 9, y + 3)
(x, y) -->
(x + 9, y - 3)
(x, y) -->
(x + 3, y - 9)
(x, y) -->
(9x, 3y)
(x, y) ----> (x - 1, y)
What are the coordinates of M'?
Select the picture showing a translation of:
4 squares right and 1 square up
Select the picture which shows a translation:
4 squares right and 5 squares down
What color is the pre-image?
blue
purple
What color is the image?
red
blue
What is another name for a translation?
Slide
Flip
Mirror
Find the image of P(3, 4) after the composition of translations (x, y)→(x+1, y−2) and (x, y)→(x−5, y+1) .
(−2, 5)
(4, 2)
(−1, 3)
(2, 6)
Find the image of D(0, −2) after the composition of translations (x, y)→(x+10, y−8) and (x, y)→(x−7, y+15) .
(3, 5)
(10, −10)
(−7, 13)
(−4, 8)
WRITE A TRANSLATION RULE FOR THE IMAGE.
(x + 3, y - 1)
(x - 3, y + 1)
(x + 2, y + 1)
(x + 5, y + 3)
D(3, 4) and D'(5, -13) are the pre-image and image of a given triangle. What is the translation?
(x, y) → (x-2, y+13)
(x, y) → (x+2, y-13)
(x, y) → (x+2, y-17)
(x, y) → (x-2, y+17)
In the figure, triangle PQR has vertices P(0, −1), Q(3, −1) and R(5, −3). What are the vertices of the image after the translation (x, y) → (x − 5, y + 1)?
P′ (1, −6), Q′ (4, −6), R′ (6, −8)
P′ (−5, 0), Q′ (−2, 0), R′ (0, −2)
P′ (5, −2), Q′ (8, −2), R′ (10, −4)
P′ (−1, 4), Q′ (2, 4), R′ (4, 2)
If the quadrilateral is translated 4 units to the left and 5 units down what is the coordinates for Point A'?
(4,0)
(0,4)
(-1,5)
(5,-1)
What happens to (-9, 3) when it is translated 4 units down and 3 units right?
(-6, -1)
(-13, 6)
(-5, 6)
(-6, 7)
Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are
(–9, 2), what are the coordinates of F'?
(–17, 5)
(–6, –6)
(–17, –1)
(–12, –6)
Rectangle ABCD has vertices A(–6, –2), B(–3, –2),
C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1),
C’(–7, –3), and D’(–10, –3).
(x, y) →(x–4, y+3)
(x, y) →(x–4, y+1)
(x, y) →(x+4, y–1)
(x, y) →(x+4, y–3)
The dashed figure is the image of the solid figure. What is the Algebraic Notation for the Translation?
(x, y) → (x - 7, y + 4)
(x, y) → (x + 7, y - 4)
(x, y) → (x + 4, y + 7)
(x, y) →(4x, 7y)
Triangle ABC has vertices at A(6, 1) B(1, 7) and C(-3, -2). The translation to create triangle A'B'C' is (x, y)(x, y) → (x - 1, y + 2). Which will be the coordinates of triangle A'B'C'?
A'(5, 2), B'(0, -4), C'(0, 9)
A'(5, 3), B'(0, -4), C'(0, 8)
A'(5, 3), B'(0, 9), C'(-4, 0)
A'(5, 2), B'(1, -3), C'(0, 9)
What is the image of the point (3, 3) under the translation (x, y)→(x+1, y−4) ?
(4, -1)
(2, 7)
(-1, 4)
(7, 2)
What is the translation rule that maps the point P (4, 1) to the point P' (-3, -5)?
(x, y)→(x − 7, y −6)
(x, y)→(x +7, y + 6)
(x, y) → (x−1, y + 4)
(x, y) → (x+1, y −4)
What is the translation rule that maps the point P (1, -1) to the point P' (-1, 5)?
(x, y)→(x − 2, y +6)
(x, y)→(x +2, y − 6)
(x, y) → (x−2, y + 4)
(x, y) → (x+1, y −4)
Determine how to translate triangle ABC to triangle A'B'C'.
(x - 9 , y + 2)
(x + 2, y - 9)
(x - 2, y + 5)
(x - 2, y + 9)
Which direction is the resultant translation?
up
down
left
right
State the image of the point.
State the image of the point.
When you rotate 180 degrees the ( x , y ) becomes ?
( y , x )
( -y , x )
( -x , y )
( -x , -y )
Rotation Rules (clockwise):
90o rotation: (x, y)→(y, -x)
What are the coordinates for A' after a 90⁰ rotation clockwise?
(1, 3)
(3, 1)
(3, -1)
(1, -3)
Rotation Rules (clockwise):
180o rotation: (x, y)→(-x, -y)
What are the coordinates of C' after a rotation of 180° clockwise?
(-3, -1)
(3,1)
(1,3)
(-1, -3)
Rotation Rules (clockwise):
270o rotation: (x, y)→(-y, x)
What are the coordinates of B' after a 270° clockwise?
(4, 4)
(4, -4)
(-3, 4)
(-4, 4)
Does the image show a rotation? If so, what is the angle of rotation?
90° counterclockwise
180° counterclockwise
270° counterclockwise
Not a rotation
Does this image show a rotation? If so, what is the angle of rotation?
90° counterclockwise
180° counterclockwise
270° counterclockwise
Not a rotation
(x, y) ---> ___________
(x, y) ---> ___________
(x, y) ---> ___________
(x, y) ---> ___________
State the image of the point.
When you rotate 180 degrees the ( x , y ) becomes ?
( y , x )
( -y , x )
( -x , y )
( -x , -y )
If (4,-2) → (4,-2) represents a counterclockwise rotation of the point on a coordinate plane, how many degrees is the rotation?
90
180
270
360
Under what composition of transformations does triangle ABC map onto triangle A''B''C''
Reflection over x-axis, then Rotation of 90 Degrees
Rotation of -90 Degrees, then Reflection over y-axis
Reflection over y-axis, then Rotation of -90 Degrees
Rotation of 90 Degrees, then Reflection over x-axis
What is the transformation from Triangle ABC to Triangle A''B''C''?
Reflection x-axis, then rotation of 180 Degrees
Reflection over y-axis, then rotation of 90 Degrees
Rotation of 90 Degrees, then reflection over x-axis
Rotation of 180 Degrees, then reflection over y-axis
A double reflection over the x- and y-axes is the same as a ____________ of ______.
Rotation of 180 Degrees
Rotation of 90 Degrees
Reflection over the x-axis
Reflection over the y-axis
(x, y) ----> (x + 2, y - 3)
What axis is the triangle being reflected over?
X-axis
Y-axis
Identify the transformation:
Rotation
Reflection
Translation
Dilation
Point A is rotated 180 degrees and then flipped over the y-axis. What is A" if A is (2,7)
(2,7)
(-2, -7)
(-2, 7)
(2, -7)
Find Q''' if Q(-3, 1) is reflected over the x-axis, then rotated 90 degrees, and then translated right 3 and up 4.
(-3, 1)
(4, 1)
(4, -1)
(-3,-1)
Triangle ABC is rotated 90 degrees and then translated up 4 and left 5. What is point A if point A''' is (1,2)?
(2, -4)
(2,6)
(4, -2)
(-2 -6)
