Dilation is a geometric transformation that changes the size of an object (enlarging or shrinking) without changing its shape. Each point on the object is mapped to a new position based on a center of dilation and a scale factor.
Given a point C as the center of dilation and a scale factor k=0. The dilation of a point with respect to center by a factor , denoted as , is a transformation that maps to such that .
A
C
k
D(C,k)
A
A′=D(C,k)(A)
CA′=k⋅CA
This means the vector from the center of dilation to the image is k times the vector from the center of dilation to the original point.
If ∣k∣>1, it is an enlargement.
If 0<∣k∣<1, it is a reduction.
If k>0, the original point and its image are on the same side of the center of dilation.
If k<0, the original point and its image are on opposite sides of the center of dilation (and the image is inverted).
Determine the image of B(2,5) under dilation D(O,3) (center at O(0,0), factor 3).
Determine the image of B(2,5) under dilation with center P(1,3) and factor 3.
A triangle with vertices A(1,1), B(3,1), and C(1,4) is dilated with respect to the origin O(0,0) by a scale factor . Determine the coordinates of the image triangle !
