Yes, Rin's dad gave Sakura as a child to the Matou family, because the Matou family didn't have a mage of their own. Sakura's purple eyes and hair are a side-effect of magical worms in her body.
I'm removing those tags, because the general policy on Danbooru is to not tag something that would likely be a spoiler. Rin and Sakura pretty much is a spoiler, albeit a minor one.