Rigid Transformations
What kind of transformation is a dilation?
A. slide a figure
B. turn a figure around a point
C. flip a figure over a reflection line
D. stretching or shrinking a figure by a scale factor
D
True or False? Dilations of an angle must be congruent to the original angle.
True
These TWO things make up the similar figures checklist.
1) Proportional corresponding sides
2) Equal corresponding angles
The image of point (-2,3) under translation T' (3, -1). What is the image of point (4,2) under the same translation?
A. (-1,6)
B. (0, 7)
C. (5, 4)
D. (9, -2)
D, since the translation rule is (x + 5, y - 4)
T (-2, 3) --> T' (3, -1)
(4,2 ) --> (9, -2)
The area of triangle ABC is 49 square inches. Under which transformation could the are of the image, triangle A'B'C', be greater than 49 square inches?
A. translation
B. Rotation
C. Reflection
D. Dilation
Dilation
Which pairs of triangles MUST be similar?
A. Both triangles are isosceles. They each have a 80°
B. Both triangles each have a 100° angle.
C. Triangle A has a 50° angle and a 90° angle. Triangle B has a 40° angles and a 50° angle.
D. Triangle A has a 45° angle and a 15° angle. Triangle B has a 90° and 15° angle.
C
Calculate the value of the scale factor between the 2 triangles
B. 3
C. 3.5
D. 4
B. 3
Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image? A(3,3) B(6,6) C(9,3)
A. A'(9,9) B'(18,18) C'(27,9)
B. A'(6,6) B'(9,9) C'(12,6)
C. A'(0,0) B'(3,3) C'(6,0)
D. A'(1,1) B'(2,2) C'(3,1)
A. A'(9,9) B'(18,18) C'(27,9)
Triangle ABC is rotated 90° clockwise and then dilated by scale factor of 2 centered at the origin. The resulting image is triangle A'B'C'. Which statement about the two triangles is true?
A. The area of △ ABC is 2 times the area of △ A'B'C'.
B. The perimeter of △ABC is 2 times the perimeter of △A'B'C'.
C. The corresponding sides of △ABC and △A'B'C' are congruent
D. The corresponding angles of △ABC and △A'B'C' are congruent
D. The corresponding angles of △ABC and △A'B'C' are congruent
On a coordinate plane, vertex B for triangle ABC is located at (2,3). Triangle ABC is dilated by a scale factor of 1/2 with the center of dilation at the origin (0,0). What are the coordinates of vertex B'?
B' (1,1.5)
State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.
A. B' (2 , 4.5)
B. B' (-8 ,-18)
C. B' (8 ,18)
D. B' (9 ,4)
C. B' (8 ,18)
Triangle DEF is similar to triangle ABC. What is a sequence of transformations that maps triangle ABC to triangle DEF?
A. Reflection then rotation
B. Rotation then dilation with scale factor of 2
C. Rotation then dilation with scale factor of 0.5
D. Rotation then translation
B. Rotation then dilation with scale factor of 2
Select ALL the true statements
A. Dilations increase/decrease the measure of angles.
B. Dilations take parallel lines to parallel lines
C. Dilation of an angle are congruent to the original angle.
D. Dilation take perpendicular lines to perpendicular lines.
B, C, D
Triangle A'B'C' is the result of a dilation of triangle ABC with the center of dilation at the origin and a scale factor of 0.5
Which is not true of the triangles in the diagram?
A. Triangle ABC is similar to triangle A'B'C' because a dilated image is similar to the original figure.
B. The ratio A'B'/AB is equivalent to the ratio A'C'/AC.
C. m∠B = m∠B'
D. AB = A'B'
D is false statement
B. 3
C. 1/3
D. 1/2
2
Figure ABCDE is transformed into Figure A'B'C'D'E' through a dilation, using the origin as the center and a scale factor of 3. What are the coordinates of C'?
A. (2,1)
B. (9,18)
C. (-18,-9)
D. (18,9)
D. (18,9)
The figure below shows two parallel lines, cut by a transversal. What is the value of x.
x = 12, 48 = 4x (corresponding angles)
12 = x
Which set of angle measures could be the interior angles of a triangle?
A. 45°, 45°, 45°
B. 45°, 35°, 100°
C. 90°, 90°, 90°
D. 180°, 100°, 80°
B, 45 + 35 + 100 = 180°
Dilations can result in a congruent and similar figure if their scale factor is this number.
1
Quadrilateral ABCD is shown on this grid. If Quadrilateral ABCD is dilated about the origin using a scale factor of 1/2 to make Quadrilateral A′B′C′D′, what will be the coordinates of A′, B′, C′, and D′?
A. A'(4,2), B'(1,4), C'(4,2), D'(2,1)
B. A'(-4,2), B'(1,4), C'(4,-2), D'(-2,1)
C. A'(-4,-2), B'(-1,-4), C'(-4,-2), D'(-2,-1)
D. A'(4,-2), B'(1,4), C'(-4,-2), D'(2,-1)
B. A'(-4,2), B'(1,4), C'(4,-2), D'(-2,1)