Geometry problems on the coordinate plane

The  exercise appears under the Geometry Math Mission. This exercise connects the geometric graphing plane with the algebraic coordinates.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine if the triangles are similar: This problem provides a reference triangle and a scaled drawing of a triangle on a coordinate plane. The student is asked to determine if the triangle in the plane is similar to the reference triangle.Gpotcp1.png
 * 2) Answer the non-pictured geometry problem: This problem provides a grid that can be used to sketch a problem, but is not necessary to use to solve. The student selects the answer to the problem from a multiple choice list.Gpotcp2.png

Strategies
Knowledge of the coordinate plane is necessary, but some of the basic analytic geometry formulas and the definitions of geometric figures are encouraged to ensure success on this exercise.
 * 1) Midpoint, distance, and slope are not necessarily needed for this exercise, but comfort with distance in particular can assist on the Determine if the triangles are similar problem.
 * 2) Triangles are similar if the side ratios are proportional. This is probably the most straightforward way to solve the first problem type. Otherwise inverse trigonometry can provide a possibility.
 * 3) The non-pictured geometry problem might be determining the type of quadrilateral defined by certain points, or checking to see if points lie on a circle. Review the definitions of quadrilaterals and remember all radii of circles are congruent to help here.

Real-life Applications

 * 1) The coordinate plane connected algebra and geometry in a fundamental way. It paved the way to calculus which has a multitude of interesting applications.
 * 2) The coordinate plane is used to represent geometric models in an algebraic medium, making calculations easier.