How do you use coordinates and algebraic techniques to interpret, represent, and verify geometric relationships?

Question

How do you use coordinates and algebraic techniques to interpret, represent, and verify geometric relationships?

Answer 1

Draw the geometric shape on a Cartesian Plane. Identify the important points of the shape with ordered pairs, (x,y). For polygons the sides are line segments and all of linear equation concepts may be used to solve problems. Shapes formed by the intersection of a double cone and a plane, called conic sections (circles, ellipses, parabolas, and hyperbolas), can also be translated and dilated with algebra once their equations are derived. More complex operations or shapes may require analysis with trigonometry or calculus.