You may want to check out the old school textbooks:
- Salmon, George. A Treatise on the Analytic Geometry of Three Dimensions. Dublin, 1882.
- Sommerville, Duncan M'Laren Young. Analytical geometry of three dimensions. The University Press, 1934.
- J. G. Semple and L. Roth. Introduction to algebraic geometry. Oxford, 1949.
Usually, these classic authors didn't like drawing pictures, and they didn't have the idea of matrix (which comes much later). So I'm not sure if you would like them. On the other hand, modern geometry books become much more abstract, and they don't necessarily mention the classic elementary results.
Personally, I find using matrix helps me a lot in understanding geometry. I benefit a lot from trying to assign geometric meaning to every word in the vocabulary of standard linear algebra and matrix analysis. The book that helps me most is:
- Pottmann, Helmut, and Johannes Wallner. Computational line geometry. Springer Science & Business, 2009.
A much easier but equally helpful book is:
- Boehm, Wolfgang, and Hartmut Prautzsch. "Geometric concepts for geometric design." (1994).
Finally, I don't really think coordinate geometry is that important, because too often the geometric meaning is lost in computation with coordinates. It is more intuitive, geometric meaningful to use geometric algebra, which is equivalent to coordinate geometry with a little bit of representation theory.