; ▁its ▁ratio ▁to ▁one ▁of ▁the ▁others ▁does ▁have ▁meaning . ▁Thus ▁" com ma ▁notation " ▁for ▁tr il ine ar ▁coordinates ▁should ▁be ▁avoided , ▁because ▁the ▁notation ▁( x , ▁y , ▁z ), ▁which ▁means ▁an ▁ordered ▁triple , ▁does ▁not ▁allow , ▁for ▁example , ▁( x , ▁y , ▁z ) ▁= ▁( 2 x , ▁ 2 y , ▁ 2 z ), ▁whereas ▁the ▁" colon ▁notation " ▁does ▁allow ▁x ▁: ▁y ▁: ▁z ▁= ▁ 2 x ▁: ▁ 2 y ▁: ▁ 2 z . ▁ ▁Ex amples ▁ ▁The ▁tr il ine ar ▁coordinates ▁of ▁the ▁in center ▁of ▁a ▁triangle ▁ABC ▁are ▁ 1 ▁: ▁ 1 ▁: ▁ 1 ; ▁that ▁is , ▁the ▁( direct ed ) ▁distances ▁from ▁the ▁in center ▁to ▁the ▁s idel ines ▁BC , ▁CA , ▁AB ▁are ▁proportional ▁to ▁the ▁actual ▁distances ▁denoted ▁by ▁( r , ▁r , ▁r ), ▁where ▁r ▁is ▁the ▁in radius ▁of ▁triangle ▁ABC . ▁Given ▁side ▁lengths ▁a , ▁b , ▁c ▁we ▁have : ▁▁ ▁A ▁= ▁ 1 ▁: ▁ 0 ▁: ▁ 0 ▁ ▁B ▁= ▁ 0 ▁: ▁ 1 ▁: ▁ 0 ▁ ▁C ▁= ▁ 0 ▁: ▁ 0 ▁: ▁ 1 ▁ ▁in center ▁= ▁ 1 ▁: ▁ 1 ▁: ▁ 1 ▁ ▁cent roid ▁= ▁b c ▁: ▁ca ▁: ▁ab ▁= ▁ 1 / a ▁: ▁ 1 / b ▁: ▁ 1 /