Reflections
Reflect the point (3, −5) across the x-axis.
(3,5)
Rotate the point (4, −1) 90° counterclockwise about the origin.
(1, 4)
Translate (2, −3) by ⟨x+4, y+2⟩.
(6, −1)
What is a line of symmetry? (short definition)
A line such that reflecting the figure across it maps the figure onto itself.
What does a scale factor k = 2 mean for a dilation about the origin?
Every coordinate is multiplied by 2; every length doubles.
Reflect the point (3, −5) across the x-axis.
(4, −2)
Rotate (−3, 5) 180° about the origin.
(3, −5)
Apply the rule (x, y) → (x − 5, y + 3) to the point (6, −1).
(1, 2)
How many lines of symmetry does a regular hexagon have?
6
Dilate the point (3, 4) about the origin by k = 1/2.
(1.5, 2)
Reflect (6, 3) across the y-axis, then reflect across the line x = −2. What are the final coordinates?
(2, 3)
Rotate (4, 2) 270° counterclockwise about the origin.
(2, −4)
ΔGHI has G(−1, 2). After a translation by ⟨x−3, y+1⟩, what are the coordinates of G′?
(−4, 3)
Name transformations that map a square onto itself.
Rotations of 90°, 180°, 270° about the center; reflections across either diagonal and across vertical/horizontal lines through the center.
7 total
An 8.5 × 11 in. page is enlarged; the shorter side becomes 10 in. What is the scale factor?
10 / 8.5 = 20/17 ≈ 1.176
Preimage A is (7, 7) and image A′ is (5, 3). Find the equation of the line of reflection.
y = (1/2)x +2
Give the rule for a 90° counterclockwise rotation, and apply it to (−5, −1).
Rule: (x, y) → (-y, x). Applied: (1, -5)
If translation maps P(−6, 2) → P′(1, 4), what is the translation rule?
(x, y) → (x + 7, y + 2)
Which composed transformations guarantee ΔMNO is congruent to ΔPQR? (choose from reflection, rotation, translation, dilation)
Any combination of reflections, rotations, and translations (but not a dilation). Example: reflection + rotation, rotation + translation.
The larger triangle is a dilation of the smaller triangle with k = 2. If a side of the small triangle is x = 3 and another side y = 5, what are the new lengths?
x′ = 6, y′ = 10
Given F(2,2) maps to G(4,10) by a reflection across some line. Determine the equation of that line of reflection.
y=(-1/4)x+(27/4)
Triangle with A(2,4), B(4,1), C(1,−2) is rotated 180° about the origin. What are A′, B′, C′?
A′ = (−2, −4), B′ = (−4, −1), C′ = (−1, 2)
Apply translation ⟨x+3, y−5⟩ then reflect across y = x to the point (2, −1). What is the final image?
(−6, 5)
A rhombus is rotated 180° about its center then reflected across one diagonal. Will the image coincide with the original? Explain.
Yes — a rhombus has 180° rotational symmetry about its center; additional reflection across a symmetry diagonal may map it onto itself depending on orientation (explain via symmetry lines).
After dilation by scale factor k, how many times is the perimeter multiplied? How many times is the area multiplied? Explain.
Perimeter multiplied by k; area multiplied by k². (Because lengths scale by k and areas scale by k×k.)