Refresher - Analytical Geometry

Analytical Geometry:

Analytical Geometry, also called co-ordinate geometry (since it takes place on a graph) or Cartesian Geometry (since it was created by René Descartes) is the study of geometry using the properties of Algebra. Descartes introduced the concept in 1637 in his book.

Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences Analytical geometry is used in cartography and navigation. The concept of longitude and latitude is also makes use of the concepts within analytic geometry. In plane analytic geometry a line can be described in terms of its slope and its y-intercept. The general equation of a line is ${\displaystyle ax+by=c}$, and the slope intercept form of a line is: ${\displaystyle y=mx+b}$ where the slope is m and the y-intercept is b. If the line is parallel to the x-axis, its slope is zero. The slope of the line through the points ${\displaystyle (x1,y1)}$ and ${\displaystyle (x2,y2)}$ is given by ${\displaystyle m=\frac{y2-y1}{x2-x1}}$.

Theory to Practice:

Two or more lines with equal slopes are parallel to one another. If the slopes are negative reciprocals (e.g., ${\displaystyle 2}$ and ${\displaystyle -\frac{1}{2}}$) then the lines are perpendicular. The distance between two points P (p, q) and Q (r, s) is found in the distance formula, which is based on the Pythagorean theorem:

${\displaystyle \overline{PQ}=\sqrt{{(p-r)}^2+{(q-s)}^2}}$