Dilatation of Two-Dimensional Transformation

Dilatation is a transformation that resizes (enlarges or shrinks) a wake, but does not change the shape of the wake.

A dilatation is determined by:

Center dilated
Dilatation factor or scale factor

1. Dilatation with center O (0, 0)

Let P'(x', y') be the shadow of the point P(x, y) by dilation by the scale factor k and center 0 as in the picture above.

Dilatation Formula with Center O(0, 0)

x' = kx + 0yy' = 0x + ky

2. Dilatation with Center P (a, b)

Dilatation with Center P(a, b) Let P'(x', y ') be the shadow of the point P(x, y) by dilation by the scale factor k and center A(a, b) as shown above.

Dilatation Formula with Center P (a, b)

x' - a = k(x - a)y' - b = k(y - b)

Example:
Please determine the shadow from point A(-2, 4) after it is dilated by a scale factor of -3 and its center P(3, -1)!

Answer:
x' - a = k(x - a)
x' - 3 = -3(-2 - 3)
x' - 3 = 15
x' - 3 + 3 = 15 + 3
x' = 18

y' - b = k(y - b)
y' - (-1) = -3(4 - (-1))
y' + 1 = -15
y' + 1 - 1 = -15 - 1
y' = -16

so the shadow is A '(18, -16).

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