A function that maps every point of a geometric figure to a new position, changing its location, orientation, or size.
Moving, rotating, flipping, or stretching a shape to produce a new image of that shape.
Showing a random 20 of 50 problems.
Example 1
medium
A figure is dilated by factor 3. Is the image congruent or similar to the original?
Example 2
easy
Translate (0,0) by the vector ⟨−3,7⟩.
Example 3
hard
After a dilation by factor −2 about the origin, where does (3,5) map?
Example 4
easy
Which three transformations are 'rigid' (preserve size and shape)?
Example 5
easy
A figure is flipped over a line. What transformation is this?
Example 6
medium
Compose two reflections across parallel lines ℓ1:x=0 and ℓ2:x=3. What is the result?
Example 7
medium
A figure is translated, then rotated. Is the final image congruent to the original?
Example 8
hard
A triangle has area 12 and perimeter 20. After dilation by factor 5, what are the new area and perimeter?
Example 9
easy
Name and describe the four basic geometric transformations.
Example 10
medium
Rotate (4,1) by 90° CCW, then translate by ⟨2,−3⟩. Find the final image.Rotate (4,1) by 90° CCW → (−1,4), then translate by ⟨2,−3⟩ → (1,1)
Example 11
easy
Apply (x,y)↦(x+4,y−2) to the point (3,5).Translation (x,y) → (x+4, y−2): find the image of (3,5)
Example 12
easy
Which transformation changes a figure's size: translation or dilation?
Example 13
medium
Point P(3,−1) is reflected over the y-axis, then translated by (2,5). Find the final image.Reflect P over the y-axis, then translate by ⟨2, 5⟩
Example 14
easy
After dilation by factor 41, what happens to a length of 20?
Example 15
easy
Reflect (4,9) across the y-axis.Reflection of (4,9) across the y-axis
Example 16
easy
Which geometric transformations are isometries (preserve distances)?
Example 17
hard
What is the image of (5,2) under a reflection across the line y=x, followed by a 90° CCW rotation about the origin?Reflect (5,2) across y=x → (2,5), then rotate 90° CCW → (−5,2)
Example 18
medium
Why does tracking only the vertices of a polygon suffice to transform the whole figure?
Example 19
hard
Two figures have areas 9 and 36 and are similar. What is the ratio of their corresponding sides?
Example 20
easy
A transformation maps (x,y)→(x+2,y−3). What type is it?