Translations
Point A is located at (3, 2). It is translated 4 units right and 5 units up. What are the coordinates of A' after the translation?
A' is located at (7, 7)
Point A(3, 2) is reflected over the line y = x. What are the coordinates of A'?
A'(2, 3)
Point A(3, 2) is rotated 90° counterclockwise around the origin. What are the coordinates of A'?
A'(-2, 3)
The original image to be transformed.
Pre Image
A (-3,2)
1. Reflected over the x axis
2. Translated (x,y) -----> (x+3, y)
What are the coordinates of A''?
A'' (0, -2)
Point A(2,−1) is translated (x, y) --> (x -4, y +7), what are the coordinates of A''?
(-2,6)
Point B(5, -3) is reflected over the line y = 1. What are the coordinates of B
B'(5, 5)
Point B(-4, 2) is rotated 270° counterclockwise around the origin. What are the coordinates of B'?
B'(2, 4)
Turning a figure around a point with a specific angle and in a specific direction.
Rotation
A (4, -7)
1. Reflect over the line y= -x
2. Reflect over the line x=1
What are the coordinates of A''
A''(-5, -4)
Point P(-2, 5) is translated to P'(3, -1). How was it translated?
(x, y) --> (x +5, y -6)
Triangle PQR has vertices P(-1, 3), Q(2, 4), and R(1, -2). If it is reflected over the line y = -x, what are the coordinates of P', Q', and R'?
P'(-3, 1), Q'(-4, -2), R'(2, -1)
Line segment CD has endpoints C(5, -2) and D(-1, 4). If it is rotated 180° counterclockwise around the origin, what are the coordinates of C' and D'?
C'(-5, 2), D'(1, -4)
A transformation that flips a figure over a line
Reflection
Line segment AB has coordinates A (0,0) and B(3, 6)
1. Rotation 180
2. Reflection over y = -x
What are the coordinates for A'' and B''
A''(0, 0) B"(6, 3)
Triangle ABC has vertices at A(0, 0), B(3, 0), and C(0, 4). If it is translated 2 units left and 1 unit down, what are the new coordinates of A', B', and C'?
A'(-2, -1), B'(1, -1), C'(-2, 3)
Square ABCD has vertices at A(0, 0), B(0, 4), C(4, 4), and D(4, 0). After reflection over the line x = 2, what are the coordinates of the reflected square?
A'(0, 4), B' (4, 4), C' (0, 4), D' (0, 0)
Triangle PQR has vertices P(1, 1), Q(3, 1), and R(2, 3). After a 90° counterclockwise rotation around the origin, what are the coordinates of P', Q', and R'?
P'(-1, 1), Q'(-1, 3), R'(-3, 2)
The resulting figure after the transformation
Image
Line Segment AB has coordinates A (-1, 3) and B(2, 0)
1. Reflect over y=1
2. Translation (x, y) --> (x+2, y+2)
3. reflect over y = -x
A''' (-1, -1) and B''' (-4, -4)
A parallelogram ABCD has vertices at A(1, 2), B(5, 4), C(7, 8), and D(3, 6). After a translation, point A' is at (4, -1). What are the coordinates of B', C', and D'?
After translation, the vertices are:
A'(4, -1), B'(8, 1), C'(10, 5), D'(6, 3)
Line segment CD has endpoints C(-2, 3) and D(4, -1). If it is reflected and the image has coordinates of
C' (8, 3) and D' (2, -1).
What is the line of reflection?
x = 3
A square has vertices at (0, 1), (2, 1), (2, 3), and (0, 3). After a 90° counterclockwise rotation around the origin, what are the coordinates of the rotated square?
(-1, 0), (-1, 2), (-3, 2), (-3, 0)
A transformation that only changes the location on the graph (orientation stays the same)
Translation
Triangle ABC has coordinates at A(-2, 4), B(0, 7), and C (4, 1)
1. Reflect over the y axis
2. Rotate 270 CCW
3. Translation (x,y) --> (x -1, y +2)
A''' (3, 0)
B''' (6, 2)
C''' (0, 6)