Rigid Transformations
Square ABCD is translated 4 units to the right and 2 units down on a coordinate grid to create square A'B'C'D'. Which rule describes this translation?
(x,y) --> (x+4, y-2)
True or False.
Dilations always keep the angles the same.
True -- when you dilate a figure, the angles will always stay the same.
True or False
Similarity means same shape & same size
FALSE
that is congruent
If a point from the pre-image is (2,-2) and a point from the image is (10,-10). What is the rule for this dilation?
(x,y)--> (5x,5y)
A figure is dilated with a scale factor of 3/2.
Is the image larger, smaller, or the same size as the original?
1.5 times larger than the original figure
A triangle is reflected over the y-axis. What rule describes this transformation?
(x,y) --> (-x,y)
True or False
Dilations never preserve congruence
False
A scale factor of 1 preserves congruence
Which statement best describes similar figures?
A. They have the same size and the same shape.
B. They have the same shape, but not necessarily the same size.
C. They have the same perimeter but different shapes.
B. They have the same shape, but not necessarily the same size.
If a point from the pre-image is (10,-10) and a point from the image is (2,-2). What is the rule for this dilation?
(x,y)--> (1/2x, 1/2y)
Which transformations are non-rigid, and why?
Dilations, because they change the size of the figure.
A trapezoid is rotated 270 degrees clockwise. What rule represents this transformation?
(x,y)--> (-y,x)
A triangle is dilated from the origin using a scale factor of 3. If one vertex is at (2, 1), what are the coordinates of the image?
(6,3)
Two rectangles are similar.
Rectangle A has a length of 6 and a width of 4.
Rectangle B has a length of 12.
What is the width of Rectangle B?
8
Scale factor = 12 ÷ 6 =2
Width = 4 × 2 = 8
A triangle is dilated with a scale factor of 1 from a center of dilation. What happens to the triangle, and why?
The triangle stays the same, because a scale factor of 1 does not change size.
Which statement is always true?
A. Dilations of a triangle keep angle measures the same.
B. Dilations of a triangle keep side lengths the same.
C. Dilations of a triangle must be congruent to the original triangle.
D. Dilations of a triangle always make the sides longer.
A - angles measurements always stay the same when dilating an image; they are similar.
Rectangle MNPQ is translated 6 units left and 7 units up. Write a rule that describes this transformation? Is congruence preserved?
(x,y)--> (x-6, y+7)
YES
A square has a vertex at (–4, 2). After a dilation centered at the origin with a scale factor of 2, what are the new coordinates?
(-8,4)
In similar figures, corresponding angles are ______ and corresponding sides are ______
Proportional
Triangle TUV is dilated with the origin as the center of dilation using the rule (x, y) → (1.7x, 1.7y) to create the triangle T′U′V′. What happens to the size of T′U′V′?
A point (6, 4) is dilated from the origin with a scale factor of 3. What are the new coordinates?
(18, 12)
Which type of transformation does NOT preserve congruence?
(rotation, reflection, translation, dilation)
Dilation
A point is located at (8, −6). It is dilated from the origin using a scale factor of ¾. What are the coordinates of the image?
(6, -4.5)
Two similar triangles have a scale factor of 2 from the smaller triangle to the larger triangle.
If the perimeter of the smaller triangle is 18 units, what is the perimeter of the larger triangle?
36 units
If a point from the pre-image is (12,8) and a point from the image is (3,2). What is the rule for this dilation?
(x,y)--> (1/4x, 1/4y)
Why is your math teacher the BEST teacher in the world?
teacher discretion