Translations
Original points to plot are (-4,3),(-2,4),and (-4,5) Translate 5 units down and 3 left. Graph on board.
(-7,-2), (-5,-1), and (-7,0)
What is a reflection?
A transformation that flips
If a point M, located at (3, -2), is rotated clockwise 90° about the origin, what are the coordinates of its image, M′?
(-2,-3)
Triangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2). Find the coordinates of the vertices of triangle A’B’C’ after triangle ABC is translated using the rule (x, y) → (x + 5, y - 3). Then describe the translation.
A’(1, -2), B’(3, -2), and C’(4, -5); The triangle is translated 5 units to the right and 3 units down.
Which transformation(s) change the orientation of figures?
Reflections and Rotations
What is a translation?
A transformation that slides
Graph triangle ABC with vertices A(-4, 1), B(-2, 1), and C(-1, -2) on a coordinate grid. Graph the image of triangle ABC after a reflection across the y-axis.
A'(4,1),B'(2,1), and C'(1,-2)
If you rotate 180 degrees does it matter if your going clockwise or counterclockwise?
NO!!
Triangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2). Find the coordinates of the vertices of triangle A’B’C’ after a 90° clockwise rotation about the origin.
A’(1, 4), B’(1, 2), and C’(-2, 1)
Translations are the only transformation that don't change orientation? True or False
TRUE
The original plotted points are (0,3),(3,3),(2,-1), and (5,-1)
Translate 5 left and 2 down. Graph on board.
(-5,1),(-2,1),(-3,-3), and (0,-3)
If a point M, 5 units from the x-axis, is reflected across the x-axis, how far is the image of the point, M’, from the x-axis?
5 units
What is a rotation?
A transformation that turns
Triangle ABC has vertices A(-2, 6), B(0, 5), and C(3, -1). Find the vertices of triangle A′B′C′ after a reflection across the x-axis.
A′(-2, -6), B′(0, -5), and C′(3, 1)
On a coordinate grid, graph a triangle with its vertices at (-2, 1), (-4, 1), and (-1, 4). Label each image with the letter of the transformation applied. A Rotation 90º clockwise around the origin
Is this congruent?
(1,2),(1,4), and (4,1)
YES
Graph triangle ABC with vertices A(-3, 4), B(0, 2), and C(-2, 1) on a coordinate grid. Graph the image of triangle ABC after a translation of 4 units right and 3 units down.
A'(1,1),B'(4,-1), and C'(2,-2)
Graph triangle DEF with vertices D(2, 6), E(5, 6), and F(5, 1) on the coordinate grid. Next graph triangle D ′E ′F ′, the image of triangle DEF after a reflection across the x-axis.
D'(2,-6),E'(5,-6),and F'(5,-1)
Graph triangle ABC with vertices A(-4, 1), B(-2, 1), and C(-1, -2) on a coordinate grid. 1. Graph the image of triangle ABC after a 180° clockwise rotation about the origin.
A'(4,-1),B'(2,-2), and C'(1,2)
Triangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2). Find the coordinates of the vertices of triangle A’B’C’ after triangle ABC is reflected across the y-axis.
. A’(4, 1), B’(2, 1), and C’(1, -2)
What is a congruent figure?
Two figures that have the same size and shape.
Graph quadrilateral KLMN with vertices K(–3, 2), L(2, 2), M(0, –3), and N(–4, 0) on the coordinate grid. On the same coordinate grid, graph the image of quadrilateral KLMN after a translation of 3 units to the right and 4 units up.
k'(0,6),l'(5,6),m'(3,1),and n'(-1,4)
Graph triangle ABC with vertices A(-4, 1), B(-2, 1), and C(-1, -2) on a coordinate grid. Graph the image of triangle ABC after a reflection across the x-axis.
A'(-4,-1), B'(-2,-1), and C'(-1,2)
A(0,0),B(1,2),C(4,2), and D(3,0)
Rotate 270 degrees clockwise
A'(0,0),B'(-2,1),C'(-2,4), and D'(0,3)
Point M has coordinates (3, -2). The coordinates of point M’ after a single transformation are (-3, 2). Name a transformation that could have done this
translation 6 units left and 4 units up; rotation of 180°; reflection across the line y = x
(x, y) → (-y, x), (x, y) → (x + 1, y)
Does the algebraic representation show a congruent figure.
YES