Category 1
This transformation slides a figure without turning or flipping it.
Translation
This transformation turns a figure around a fixed point.
Rotation
This transformation flips a figure over a line.
Reflection
What does a scale factor greater than 1 do to a figure?
Enlarge
Which transformations are rigid motions?
Translations, Reflection, Rotation ( Rigid does NOT change shape or size only position )
Translate point A(2, −1) right 3 units and up 2 units.
A'(5 , 1)
A figure is rotated 90° clockwise about the origin. Where does (3, 2) go?
( x , y ) → ( -y , x ) → ( 2 , -3 )
Reflect point (−6, 2) over the x-axis.
( x , y ) → ( x , -y ) → (-6 , -2 )
What does a scale factor greater than 1 do to a figure?
( x , y ) ( kx , ky )
k = scale factor
A figure is dilated by 3 and then translated left 4 units. Which step changes size, and which does not?
What is the rule for a translation left 5 units and down 4 units?
( x - 5 , y - 4 )
What rule represents a 180° rotation about the origin?
( x , y ) to ( - x ,- y )
Write the rule for reflecting a point across the y-axis.
( x , y ) → ( -x , y )
Dilate point (−3, 4) by a scale factor of ½ about the origin.
( 1.5 , 2 )
A triangle has side length 5. After dilation, the side length is 15. What was the scale factor?
3
A point moves from (3, −4) to (−1, 2). What translation occurred?
Left 4 Up 6
A point at (−5, 4) is rotated 90° counterclockwise. What is the image?
(x, y) → (-y, x) → (-4 , 5 )
A point (5, −3) is reflected over the line y = x. What is the image?
( x , y ) → ( y , x ) → ( -3 , 5 )
A point (−6, 2) is dilated by a scale factor of 3 about the origin. What is the image?
( -18 , 6 )
Which transformations preserve distance?
Reflection
A figure is translated using (x + 2, y − 7). If one vertex is at (−5, 6), what is the image?
( -3, -1 )
A figure is rotated about the origin and maps (x, y) → (y, −x). What was the degree and direction of rotation?
90-degree clockwise rotation
A point is reflected across the line y = x. If the image is (4, −1), what was the original point?
( x , y ) → ( y , x ) → ( -1 , 4 )
A dilation does not change shape but does change size. What property stays the same?
Shape
A point (2, −5) is reflected over the y-axis and then rotated 180° about the origin. What is the final image?
( -5 , 2 )