If a figure has coordinates A (-2, -6), B (-1, -3) and C (0, -6), what would the coordinates of the new figure be if it was translated 2 units right and 4 units down?
A’ (0, -10), B’ (1, -7), and C’ (2, -10)
100
If a figure has coordinates A (-4, -2), B (-3, 1) and C (-2, -2), what would the coordinates of the new figure be if it was reflected across the y-axis?
A’ (4, -2), B’ (3, 1), and C’ (2, -2)
100
If a figure has coordinates E (2, -4), F (-1, 3) and G (2, -2), what would the coordinates of the new figure be if it was rotated 90⁰ clockwise around the origin?
E’ (-4, -2), F’ (3, 1), and G’ (-2, -2)
100
What is a translation?
A translation preserves a figure's _____ and a figure's _____, which means _________ and ________.
The pre-image and new image are ___________.
Translation: when a figure is moved in any direction. A slide!
A translation preserves the figure's shape and the figure's size, which means angles are the same measure and line segments are the same length.
CONGRUENT!
100
If the measure of
The measure of
200
A triangle has coordinates A (-3, -2), B (-2, 2) and C (0, 2). If the triangle is translated 3 units up and 5 units left, what would the coordinates of the new triangle be?
A' (-8, 1), B' (-7, 5), and C' (-5, 5)
200
A figure has coordinates K(2, -4), L(3, -4), M(-5,6) and N(-3,6). If the figure was reflected across the x-axis, what would the coordinates of the new figure be?
K' (2, 4), L' (3, 4), M' (-5, -6), and N' (-3, -6)
200
A figure has coordinates D (1, -3), E (1, 1), F (3, 1), and G (-3, -3). If the figure was rotated 180°, what are it's new coordinates?
D' (-1, 3), E' (-1, -1), F' (-3, -1), and G' (3, 3)
200
What is a reflection?
A reflection preserves a figure's _______ and a figure's _______, which means ________ and ________.
The pre-image and new image are ________.
A reflection is a mirror image, a flip over a given line.
A reflection preserves the figure's shape and the figure's size, which means angles are the same measure and line segments are the same length.
CONGRUENT!!
200
Draw triangle XYZ on the graph:
X (-6, -2), Y (-4, -3), Z (-3, 2)
Translate this triangle using the rule (x + 5, y + 4).
Then, translate image X'Y'Z' using the rule (x + 3, y - 6).
What are the coordinates of X''Y''Z''?
X'' (2, -4), Y'' (4, -5), Z'' (5,0)
300
Triangle HIJ had coordinates H (3, -2), I (4, -3) and J (6, 3). It was translated to a new position with coordinates H’ (5, -7), I’ (6, -8) and J’ (8,-2). What is the rule that was used to translate the figure? Express your answer in translation notation.
2 units right and 5 units down.
(x + 2, y - 5)
300
Triangle ABC had coordinates A (3, -2), B (4, -3) and C (6, 3). It was reflected to a new position with coordinates A’ (3, 2), B’ (4, 3) and C’ (6, -3). What is the rule that was used to reflect the figure?
A reflection across the x-axis.
300
A trapezoid has vertices Q (-2, 5), R (3, 5), S (6, 1), and T (-2, 1). What are the new coordinates of the figure after a 90° rotation counterclockwise?
Q’ (-5, -2), R’ (-5, 3), S’ (-1, 6), and T’ (-1, -2)
300
What is a rotation?
A rotation preserves the figure's _______ and the figure's _______, which means _______ and ________.
The pre-image and new image are ________.
A rotation is a turn around a fixed point.
A rotation preserves the figure's shape and the figure's size, which means angles are the same measure and line segments are the same length.
CONGRUENT!!
300
Graph Triangle ABC with coordinates A (5,1) B (1,2) and C (6,2).
Graph Triangle A'B'C', the image of triangle ABC after being reflected in the x-axis.
Graph Triangle A''B''C'', the image of triangle A'B'C' after being translated with the rule (x - 10, y + 4).
What are the coordinates for Triangle A''B''C''?
A'' (-5, 3), B'' (-9, 2) C'' (-4, 2)
400
Vector FG can be expressed as (x + 2, y + 3). Translate triangle ABC along this vector. What are the coordinates of the new triangle?
A (-6, 2), B (-8, -2), C (-7, -4)
A' (-4, 5), B' (-6, 1), C' (-5, -1)
400
Triangle PQR has vertices P (0,0), Q (5, -2), and R (-3, 6). Find the vertices of triangle P'Q'R' after a translation of 8 units left and 1 unit down.
Translate P'Q'R' 2 units to the right and 5 units up. What are the coordinates of the new triangle P''Q''R''?
P'' (-6, 4), Q'' (-1, 2), R'' (-9, 10)
400
Figure QRST has vertices Q(2,-1), R (6,-1), S(6,-3) and T(2,-3). Which will be the coordinates of point R after the rectangle is rotated 90º counterclockwise about the origin?
R' (1,6)
400
If a figure begins in Quadrant 1 and is reflected first over the x-axis and then over the y-axis, what Quadrant is the final figure in?
Quadrant 3
400
Triangle JKL has vertices J (-7, 4), K (7,1) and L (2, -2). Find the new coordinates of the vertices of the triangle after a reflection first over the x-axis and then over the y-axis.
x-axis: J' (-7, -4) K' (7, -1) L' (2,2)
y-axis: J'' (7, -4) K'' (-7, -1) L'' (-2, 2)
500
Rectangle ABCD has coordinates A (1,3) B (1,7) C (7,7) and D (7, 3)
Translate Rectangle ABCD 3 units down and 4 units left. What are the new coordinates of the rectangle A'B'C'D'?
A' (-3,0)
B' (-3, 4)
C' (3, 4)
D' (3, 0)
500
Reflect ∆XYZ over the vertical line (parallel to the y-axis) through the point (-1, 0). Label the reflected image X'Y'Z'. What are the coordinates of the new triangle?
X (5,5), Y (6,2), Z (2,3)
X' (-7, 5) Y' (-8, 2) Z' (-4,3)
500
Graph ∆JKL after a rotation of 180º about the origin. J(5,6) K(7,9) L (1,2). What are the coordinates of the new figure?
J(-5,-6), L(-7,-9), L(-1,-2)
500
Explain the difference between a rigid transformation and non-rigid transformation.
A rigid transformation does not change the size or shape of a figure.
A non-rigid transformation does change size, but NOT shape of a figure.
500
Triangle RST has coordinates R (-2, 5) S (-1, 2) and T (-5, 1)
Rotate Triangle RST 180 degrees.
Translate R'S'T' 2 units up. What are the new coordinates of Triangle R''S''T''?