Transformations
What transformation slides a figure without turning or flipping it?
Translation
In the point (6, −2), what is the x-coordinate?
6.
What is the sum of the interior angles of a triangle?
180°
A dilation has scale factor 2. Does the image become larger or smaller?
Larger.
True or false: Similar figures have the same shape but may have different sizes.
True.
A figure is reflected across a line. What happens to its size and shape?
They stay the same; reflection is a rigid transformation.
Point (3, 4) moves 5 units left. What is its new location?
(−2, 4)
Two angles in a triangle measure 45° and 65°. Find the third angle.
70°.
A 7 cm side is dilated by scale factor 3. What is the new length?
21 cm.
A triangle has sides 3, 4, 5. A similar triangle has sides 6, 8, and what?
10.
A figure is rotated 90° clockwise around the origin. Where does (2, 5) move?
(5, −2). The rule is (x, y) → (y, −x).
Reflect (−5, 3) across the x-axis. What is the image?
(−5, −3)
Two parallel lines are cut by a transversal. One angle measures 118°. What is its corresponding angle?
118°
Point (4, −6) is dilated by 1/2 about the origin. Find the image.
(2, −3).
Are triangles with side lengths 4, 6, 8 and 6, 9, 12 similar?
Yes. All corresponding side ratios equal 3/2.
A triangle is translated, reflected, and rotated. Its original perimeter is 27 cm. What is the image's perimeter?
27 cm. Rigid transformations preserve side lengths.
A point moves from (−2, 7) to (4, 1). Describe the translation.
6 units right and 6 units down
Two parallel lines are crossed by a transversal. One angle measures 65°.
What are the measures of the angles that are supplementary to it?
Answer: 115° each.Supplementary angles add up to 180°, so 180° − 65° = 115°.
A rectangle measuring 8 by 12 is dilated to 14 by 21. What is the scale factor?
7/4 or 1.75.
A 5-by-8 rectangle is similar to one with width 15. Find the larger rectangle's length.
24, because the scale factor is 3.
A point (−3, 4) is rotated 90° counterclockwise and then reflected across the y-axis. What are its final coordinates?
(4, −3). First rotate to (−4, −3), then reflect to (4, −3).
Point P(−6, 8) is dilated by 1/2 about the origin and then translated 4 units right. What is P′?
(1, 4). Dilation gives (−3, 4), then translation gives (1, 4).
A triangle has angles measuring 45°, 65°, and 70°. It is reflected across the y-axis and then rotated 90° clockwise.
What are the three angle measures of the final triangle? Explain why.
45°, 65°, and 70°.Reflections and rotations are rigid transformations. They preserve angle measures, so the final triangle is congruent to the original.
A triangle has perimeter 36 cm and area 54 cm². It is dilated by scale factor 2/3. Find the new perimeter and area.
Perimeter = 24 cm; area = 24 cm². Perimeter scales by 2/3 and area by 4/9.
Two triangles have side lengths 6, 9, 12 and 10, 15, 20. Are they similar? Give the scale factor from the first to the second and justify.
Yes. The corresponding ratios are 10/6 = 15/9 = 20/12 = 5/3, so the scale factor is 5/3