# Homothety: Creates an homothety from a given polygon In LearnGeom: Learning Plane Geometry

## Description

`Homothety` creates an homothety from a given polygon

## Usage

 `1` ```Homothety(Poly, C, k, lines = F) ```

## Arguments

 `Poly` Polygon object, previously created with function `CreatePolygon` `C` Vector containing the xy-coordinates of the center of the homothety `k` Number which represents the expansion or contraction factor for the homothety `lines` Boolean. When `lines` = `TRUE`, the plot displays the lines that connect the center of the homothety with the points of the polygons (the original and the transformed one). If missing, it works as with `lines` = `FALSE`, so the lines are not displayed

## Value

Returns the coordinates of a polygon that has been transformed according to the homothethy with center at `C` and factor `k`

## References

https://www.encyclopediaofmath.org/index.php/Homothety

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```x_min <- -2 x_max <- 6 y_min <- -3 y_max <- 5 CoordinatePlane(x_min, x_max, y_min, y_max) P1 <- c(0,0) P2 <- c(1,1) P3 <- c(2,0) Poly <- CreatePolygon(P1, P2, P3) Draw(Poly, "blue") C <- c(-1,-2) k1 <- 0.5 Poly_homothety1 <- Homothety(Poly, C, k1, lines = TRUE) Draw(Poly_homothety1, "orange") k2 <- 2 Poly_homothety2 <- Homothety(Poly, C, k2, lines = TRUE) Draw(Poly_homothety2, "orange") ```

### Example output

```NULL
[1] "Some of the inserted points are collinear. This could lead to a defective polygon."
NULL
NULL
NULL
```

LearnGeom documentation built on July 14, 2020, 5:06 p.m.