Translations
What does a translation do to a figure?
It slides the figure without changing its size or orientation
What is a reflection?
A reflection flips a figure over a line, creating a mirror image.
What does a rotation do to a figure?
A rotation moves around the orgin in a clockwise or counter clockwise direction.
What does it mean for two figures to be congruent?
The have the same size and the same shape.
Describe the sequence of transformations needed to map a triangle onto itself if it's reflected over the x-axis and then rotated 180° around the origin.
Reflect over the x-axis, then rotate 180°.
Translate the point (3, 5) by the rule (x + 2, y - 4). What is the new point?
(5, 1)
Reflect the point (2, -3) over the x-axis. What is the new point?
(2, 3)
True or False: A 360 degree rotation brings a figure back to its original position.
TRUE
True or False: Congruent figures have equal angles and corresponding sides that are equal in length.
True
A figure is reflected over the y-axis and then translated 3 units to the right. Write the coordinate rule for the transformation.
(x, y) → (-x + 3, y)
If triangle ABC is translated 3 units to the right and 2 units up, how would you describe the translation?
If triangle ABC is translated 3 units to the right and 2 units up, how would you describe the translation?
Reflect the point (-4, 7) over the y-axis. What is the new point?
(4, 7)
Rotate the point (3,4) 90 degrees counter clockwise around the orgin. What is the new point?
(-4, 3)
If two triangles are congruent, what can you say about their corresponding angles?
The are equal.
Can a figure that has been rotated 90° and then translated be congruent to its original shape? Explain.
Yes, because both rotations and translations preserve congruence.
True or False: A translation preserves the orientation of a figure
True
Reflect the point (-5, 3) over the y axis. What is the new point?
(5, 3)
What happends to the coordinates of a point after a 180 degree rotation about the orgin?
(x, y) ---> (-x, -y)
Can a figure be congruent to another if it is reflected or rotated? Explain.
Yes, because reflections and rotations preserve size and shape, keeping the figures congruent.
Describe a sequence of transformations that maps the point (1, 2) to (-2, -1)
Rotate the point 90° clockwise, then reflect it over the x-axis.
How can you describe a translation of 4 units to the left and 5 units down using a coordinate rule?
(x - 4, y - 5)
Plot a triangle ABC: A (2,1), (5,1) (3,4) and reflect it over the y axis. What are the new points of triangle ABC'?
A' (-2, 1), B' (-5,1), C' (-3, 4)
A triangle is rotated 270 degrees counter clockwise. What is the coordinate rule for this transformation?
(x, y) ---> (y,, -x)
You have two congruent triangles, one is the image of the other after a translation. What can you say about their side lengths.
Their corresponding side lengths are equal.
A figure begins in Quadrant I and reflects over the x axis and then rotates 180 degrees. What quadrant does it end in?
Quadrant II