# Homothetic property

• Apr 30th 2013, 10:04 PM
kezman
Homothetic property
I need to prove or disprove the following.

a_1 a_2 real numbers.
x, y both in R^3.
A is a convex set in R^3.

a.x in a.A and b.y in b.A. Then ax + by is in (a+b)A

(a.A, b.A, (a+b)A are all Homothetic transformations)
• Apr 30th 2013, 11:28 PM
Gusbob
Re: Homothetic property
Consider the unit vectors $v_1=(1,0,0)$ and $v_2=(0,1,0)$ and the set $A=\{a\cdot v_1|a\in \mathbb{R}\}\cup \{b\cdot v_2|2\in \mathbb{R}\}$
• May 1st 2013, 12:56 AM
kezman
Re: Homothetic property
Im sorry I forgot that A is a convex set