Singles
Point A(5, -2) is reflected over the x-axis. What are the new coordinates?
(5, 2)
If a dilation is performed with a scale factor of k = 4, is the resulting image an enlargement or a reduction?
Enlargement
A 5-foot-tall student casts a 2-foot shadow. At the same time, a nearby tree casts a 10-foot shadow. How tall is the tree?
25 feet
Point D(1, 1) is reflected over the y-axis, then translated 3 units down. What is D''?
D''(-1, -2)
Figure A is in Quadrant I. It is rotated 90 degrees CW, then 180 degrees, then 90 degrees CCW. Which Quadrant is it in now?
Quadrant III—the 90s cancel out, leaving just the 180)
What is the specific algebraic rule for a translation that moves a figure 4 units left and 7 units up? (Write in translation notation)
(x - 4, y + 7)
Point C(10, -5) is dilated with a scale factor of k = 1/5 centered at the origin. What is C'?
(2, -1)
Two triangles are similar. Triangle A has sides 3, 4, 5. The shortest side of Triangle B is 9. What is the length of Triangle B's hypotenuse?
15
A figure is rotated 90 degrees CW and then reflected over the x-axis. Is this the same as reflecting over the x-axis and then rotating 90 degrees CW?
No, the order matters!
If a figure is translated by (x+3, y-4) and then translated again by (x-3, y+4), where is the figure in relation to its start?
Back at the original starting position.
A figure is rotated 180 degrees about the origin. If a pre-image point is (x, y), what is the rule for the image point?
(-x, -y)
A line segment 8 cm long is dilated to be 20 cm long. What is the scale factor (k)?
k = 2.5 or 5/2
To measure a building's height, you place a mirror 20m from the building. You stand 4m back from the mirror. If your eyes are 1.5m high, how tall is the building?
7.5 meters
Point E(2, 4) is dilated by k=2 and then rotated 180 degrees about the origin. What is E''?
E''(-4, -8)
Find the sequence: F(2, 2) --> F'(-2, 2) --> F''(-4, 4). What two transformations occurred?
Reflection over y-axis, then Dilation k=2
Point B(3, 4) is rotated 90 degrees counterclockwise about the origin. What are the new coordinates?
(-4, 3)
True or False: A dilation preserves the congruency of the shape.
False. It preserves shape/angles, but not size/distance.
A map has a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, how far apart are they in real life?
175 miles
Triangle ABC is reflected over the y-axis and then reflected over the x-axis. This is equivalent to what single rotation?
180 degrees rotation about the origin. CW or CCW.
A triangle with vertices (0,0), (2,0), and (0,2) is dilated by k=3. What is the perimeter of the new triangle?
Answer: $6 + 6 + sqrt 72 or approx 20.48 units
Point K is located at (7, -4). It is reflected over the x-axis, then reflected over the y-axis, and finally reflected over the x-axis again. What are the final coordinates of K'?
(-7, -4)
A triangle has a base of 12 inches and a height of 8 inches. It is dilated by a scale factor of k = 3/4. What is the area of the new, smaller triangle?
27 square inches
A 12-foot ladder touches a wall 10 feet up. A smaller 6-foot ladder is leaned at the same angle. How high up the wall does the smaller ladder reach?
5 feet
Apply (x, y) --> (x+2, y) then rotate 90 degrees CCW to the point (-2, 5). What is the final location?
(-5, 0)
Point W is located at (3, -5). It undergoes the following sequence:
Rotate 90 degrees Clockwise about the origin.
Reflect over the y-axis.
Translate using the rule (x, y) --> (x+4, y+2).
What are the exact coordinates of W'''?
(9, -1)