Coordinate Dilation Calculator
Apply scale factor (k) to dilate points on coordinate plane.
Coordinate Dilation Formula
Dilated Point: (x', y') = (kx, ky)
Distance from Origin: d = √(x² + y²)
New Distance: d' = k × d
Dilation Examples
| Original Point | k | Dilated Point | Type |
|---|---|---|---|
| (2, 3) | 2 | (4, 6) | Enlargement |
| (4, 6) | 0.5 | (2, 3) | Reduction |
| (5, 0) | -1 | (-5, 0) | Reflection |
Frequently Asked Questions
What is coordinate dilation?
Dilation is a transformation that resizes a point (x,y) by multiplying both coordinates by scale factor k. New point: (kx, ky). Center of dilation is the origin (0,0).
How do I dilate a point?
Multiply x-coordinate by k and y-coordinate by k. Point (3, 4) dilated by k=2 becomes (6, 8). Works for all scale factors > 0.
What happens if k > 1?
Point moves farther from origin (enlargement). Example: (2, 3) with k=3 becomes (6, 9), which is farther away.
What happens if 0 < k < 1?
Point moves closer to origin (reduction). Example: (4, 6) with k=0.5 becomes (2, 3), which is halfway closer.
What if k = 1?
Point stays in the same location (no dilation, congruent transformation).
Can scale factor be negative?
Yes. Negative k causes both dilation and reflection through origin. Point (2, 3) with k=-2 becomes (-4, -6) (opposite side, double distance).
Does dilation change the shape of a figure?
No. All distances from origin multiply by |k|, angles stay the same. The figure maintains its shape but changes size.
What is the center of dilation?
The point from which all distances scale. In coordinate dilation, center is typically the origin (0,0). Other centers require translation.
How do I dilate a polygon?
Apply the same dilation formula to each vertex. Dilate (x1,y1), (x2,y2), (x3,y3) separately to get new vertices.
How do I find the original point if I know the dilated point?
Divide dilated coordinates by k. If dilated point is (8, 12) and k=2, original was (8/2, 12/2) = (4, 6).