What you’ll learn
Dilate figures on coordinate plane.
Key idea
A dilation about the origin multiplies both coordinates by the same positive factor; it is not a vector addition.
Both coordinates share one scale; squared pairwise distances scale by its square.
Worked example
Enter the exact value or ordered values in the format requested below.
Read image I of P after dilation factor 1/2 centered at origin. Enter image coordinate.
Marked coordinates: I=(-1, -1); P=(-2, -2).
- Origin-centered dilation multiplies each coordinate by 1/2.
- Vertices [(-2, -2), (0, -2), (-2, 0)] map to [(-1, -1), (0, -1), (-1, 0)]; every pairwise length scales by 1/2, while corresponding angles are preserved.
Answer: (-1,-1)
Quick Check
Relate the graph used in 'Dilate figures on coordinate plane' to an equation, table, transformation, or verbal description.
Connect mapping table [((4, -2), (8, -4)), ((6, -2), (12, -4)), ((4, 0), (8, 0))] and image graph to a common dilation rule.
Marked coordinates: P=(4, -2); I=(8, -4).