A rigid transformation that slides every point of a figure the same distance in the same direction.
Sliding a chess piece straight across the board—every point moves the same amount, same direction.
Showing a random 20 of 50 problems.
Example 1
hard
A translation maps the circle (x−1)2+(y+2)2=9 to a circle centered at (7,4). What is the translation vector?Circle centered at (1, −2) translates to center (7, 4) — find the vector
Example 2
medium
After translating by ⟨3,−4⟩, then by ⟨−1,6⟩, what single translation vector has the same effect?
Example 3
easy
Point P(4,7) is translated to P′(1,3). What is the translation vector?P maps to P′ — find the translation vector
Example 4
medium
A figure with vertex A(5,2) is translated so A→A′(−1,6). Where does the vertex B(3,−4) go under the same translation?Same translation maps A → A′; find where B goes
Example 5
medium
Does a translation change a figure's area?
Example 6
easy
What is the translation vector that leaves every point fixed?
Example 7
medium
Translate the parabola y=x2 by ⟨3,−2⟩. Write the equation of the image.
Example 8
easy
Does a translation change the size or shape of a figure?
Example 9
hard
A square with vertices (1,1), (3,1), (3,3), (1,3) is translated so that the bottom-left corner moves to (0,0). Find the new vertices and the translation vector.Square slides until its bottom-left corner reaches the origin
Example 10
challenge
A repeating wallpaper pattern looks identical after sliding it 5 cm right. What is this property called, and what does it imply about sliding it 10 cm right?
Example 11
medium
A figure is translated by ⟨a,b⟩. What single translation undoes it?
Example 12
challenge
Suppose translation T1 takes (0,0)→(3,4) and translation T2 takes (3,4)→(−1,7). Find the single translation equivalent to T2∘T1 and the total distance traveled by the origin.T₁ takes O→P, T₂ takes P→Q — find the combined single translation
Example 13
medium
Triangle has vertices (1,1), (4,1), (1,5). Translate by ⟨2,3⟩. Find the new vertices.Triangle translated by ⟨2, 3⟩
Example 14
medium
Translation is an isometry. What does isometry mean?
Example 15
medium
Why does a translation never have a fixed point (a point that maps to itself), unless the shift is zero?
Example 16
medium
A circle of radius 3 centered at (2,−1) is translated by ⟨4,6⟩. What is the center of the image circle, and what is its radius?Circle of radius 3 at (2, −1) translates to center (6, 5)
Example 17
medium
A figure is translated by ⟨3,2⟩, then by ⟨−1,4⟩. Find the single equivalent translation.Two successive translations — what single vector has the same net effect?
Example 18
easy
Translate the point (2,5) by 3 right and 2 up.Translate (2, 5) by 3 right and 2 up
Example 19
challenge
Prove that the composition of two translations is itself a translation, and find the vector.
Example 20
easy
A translation rule is (x,y)→(x−4,y+1). Which way does it move points?