Translations
The triangle ABC with vertices A(2, 4), B(3, 8), and C (0, 5) is translated according to the rule:
(x, y) --> (x - 2, y + 1)
What are the new vertices?
A'(0, 5), B'(1, 9), C'(-2, 6)
The triangle ABC with vertices A(2, 4), B(3, 8), and C (0, 5) is reflected across the line y = -1
What are the new vertices?
A'(2, -6), B'(3, -10), and C'(0, -7)
A clockwise rotation of 90 degrees in the same as a counterclockwise rotation of how many degrees?
270 degrees
The triangle ABC with vertices A(2, 4), B(3, 8), and C (0, 5) is dilated by a scale factor of k = 1/2
What are the new vertices?
A'(1, 2), B'(1.5, 4), C'(0, 2.5)
How many lines of symmetry does a square have?
4
The line PQ with endpoints P(-2, 7) and Q(-4, 1) is translated such that it creates the vector <4, 2> with it's image.
What are the endpoints of P'Q'?
P'(2, 9) and Q'(0, 3)
The line PQ with endpoints P(-2, 7) and Q(-4, 1) is reflected across the line y = -x
What are the endpoints of P'Q'?
P'(-7, 2) and Q'(-1, 4)
For rotations about the origin, which rotation creates the following rule:
(a, b) --> (-b, a)
Counterclockwise rotation of 90 degrees
A polygon is dilated using a scale factor k = -2. Is the image a reduction or an enlargement?
Enlargement
True or False: All similar polygons are also congruent
False; All congruent polygons are similar but not all similar polygons are congruent
(x, y) --> (x - 2, y + 4)
When reflecting across the y-axis, which variable goes negative: the x-variable or the y-variable?
The x-variable
A triangle ABC with vertices A(2, 5), B(3, 9) and C(0, 4) is rotated counterclockwise 180 degrees about the origin.
What are the vertices of the rotated image A'B'C'?
A'(-2, -5), B'(-3, -9), and C'(0, -4)
For a dilation about point P, triangle ABC is enlarged to form triangle A'B'C'. The length of PA = 4 and the length PA' = 12.
What is the scale factor k?
k = 3
How many lines of rotational symmetry does a regular five-cornered star have?
4
The polygon JKLM with vertices J(10, 2), K(11, 7), L(3, 9), and M(1, 1) is translated and forms an image J'K'L'M' with vertices J'(5, 4), K'(6, 5), L'(-2, 11), and M'(-4, 3).
What is the rule that it was translated by?
(x, y) --> (x - 5, y + 2)
The polygon JKLM with vertices J(2, 10), K(7, 11), L(9, 3), and M(1, 1) is reflected across some line and forms an image J'K'L'M' with vertices J'(10, 2), K'(11, 7), L'(3, 9), and M'(1, 1).
What is line was it reflected across?
y = x
The base of a flag is planted in the negative x-axis. After a counterclockwise rotation of 180 degrees, what axis is it planted in?
a. the positive x-axis
b. the negative y-axis
c. the positive y-axis
d. none of the above
a.
For scale factors that fall in the following range: -1<k<0 and 0<k<1
Will the images be enlargements or reductions?
Reductions
Describe the SINGLE transformation that maps JKL onto MNP where JLK has vertices J(1,1), K(2, 5), and L(5, 2) and MNP has the vertices M(1, -1), N(5, -2), P(2, -5)
Counterclockwise rotation of 270 degrees
The polygon QRST and it's image Q'R'S'T' form the vector <3, -3> between each of its corresponding points.
If the vertices of the image Q'R'S'T' are Q'(1, 2), R'(3, 7), S'(9, 8), and T'(8, 4), what are the vertices of QRST?
Q(-2, 5), R(0, 10), S(6, 11), T(5, 7)
Polygon POLY has vertices P(1, 1), O(5, 1), L(5, 7), and Y(2, 9). Give the vertices of the image after the following transformations:
Translation (x, y) --> (x - 2, y - 1)
Reflection y = 1
P'(-1, 2), O'(3, 2), L'(3, -4), and Y'(0, -6)
Polygon POLY has vertices P(1, 1), O(5, 1), L(5, 7), and Y(2, 9). Give the vertices of the image after the following transformations:
Translation (x, y) --> (x - 2, y - 1)
Rotation counterclockwise 90 degrees
P'(0, -1), O'(0, 3), L'(-6, 3), Y'(-8, 0)
Polygon POLY has vertices P(1, 1), O(5, 1), L(5, 7), and Y(2, 9). Give the vertices of the image after the following transformations:
Reflection y = x
Dilation k = 2
Triangle DEF is reflected across line k and then again across line l. The angle formed between line k and line l is 35 degrees.
Describe the single transformation that would map DEF onto its second image D"E"F".
Rotation of 70 degrees