Translation
If point A(2,3) is translated 4 units left and 2 units up, what are the coordinates of its image A′?
(−2,5)(−2,5)
What is the algebraic coordinate rule for reflecting a point (x,y) over the x-axis?
(x,−y)
A figure is rotated 180 degrees clockwise around the origin.What is the rule?
(-x, -y)
If a geometric figure on a coordinate grid is dilated about the origin by a scale factor of k=3, does this represent an enlargement or a reduction?
Write the rule.
enlargement
(3x, 3y)
Which of the four transformations does NOT preserve congruence?
dilation
A figure is translated using the coordinate rule (x,y)→(x+3,y−5). If the translated image vertex is at (1,−2), what were the coordinates of the original pre-image vertex?
(−2,3)
A triangle has a vertex at B(−1,−4). If the triangle is reflected over the y-axis, what are the coordinates of the image vertex B′?
(1,−4)
What are the coordinates of point P(3,−4) after a rotation of 180 degrees about the origin?
(−3,4)
A triangle has a vertex at D(4,−8). If the triangle is dilated and the vertex is now at (2, -4), what is the scale factor of the dilation?
k= 1/2 or 0.5
f two figures are congruent after a series of rigid transformations, what is true about their corresponding angle measures and corresponding side lengths?
they are equal (congruent)
If point E(0,−5) is translated using the coordinate rule (x,y)→(x+2,y−3), what are the coordinates of its image E′?
(2,−8)
What are the coordinates of point F(3,5) after it is reflected over the y-axis?
(−3,5)
What is the algebraic coordinate rule for a 90 degrees clockwise rotation about the origin?
(y,−x)
Write the algebraic coordinate rule representing a dilation centered at the origin with a scale factor of m.
(mx, my)
True or False: A dilation centered at the origin preserves all angle measures of the original figure, but changes its side lengths proportionally.
true
A shape is shifted 6 units right and 4 units down. What is the algebraic coordinate rule for this transformation?
(x+6,y−4)
Point G(−2,4) is reflected over the line y=x. What are the coordinates of the image G′?
(4,−2)
What is the algebraic coordinate rule for a 90 degrees counterclockwise rotation about the origin?
(-y, x)
A line segment with a length of 6 units is dilated with a scale factor of k=2. What is the length of the new dilated image segment?
12 units
Name the three transformations that are classified as "rigid motions" because they preserve both size and shape.
translations, reflections, and rotations
If a triangle is translated such that the vertex (2, 1) is moved to (0, 4), what was the specific translation rule applied?
(x−2, y+3)
Point C(2,5) is reflected over the x-axis, and then its image is translated using the rule (x,y)→(x−4,y+3). What are the final coordinates of point ′C′′?
(−2,−2)
What is the algebraic coordinate rule for a 270 counterclockwise rotation about the origin?
(y, -x)
An image vertex is located at M′(−3,6) after a dilation centered at the origin with a scale factor of 3. What were the coordinates of the original pre-image vertex M?
(-1, 2)
How do you find scale factor (k)?
k= new/old
or
k=image/pre-image