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### ANALYTIC GEOMETRY COLLEGE GEOMETRY

:Representation of Geometric Concepts The graduate applies algebraic language in representing geometric concepts to solve two-dimensional problems. 2040.1.4 : Polygon and Polyhedron Properties and Theorems The graduate applies geometric properties to solve problems.

#### INTRODUCTION

Analytic geometry provides an alternative approach to solving problems and doing proofs. Because situations are always interpreted as happening on the coordinate plane in analytic geometry, vertices can be given coordinates; thus, the tools of algebra and measurement can be used. The permitted analytic methods of proof include the midpoint formula, the distance formula, and the slope formula. In this task, you will use the figure and corresponding information in the “Analytic Geometry Graph and Permitted Analytic Methods” attachment to determine qualities of the figures on the graph.

Analytic Geometry Graph and Permitted Analytic Methods

1. Compute the coordinates for point M, showing and explaining all work.

2. Demonstrate that ?SKP is an isosceles right triangle by doing the following: a. Demonstrate that the triangle in part A2 is an isosceles triangle, showing and explaining all work. b. Demonstrate that the triangle in part A2 is a right triangle, showing and explaining all work.

3. Demonstrate that ?MNQP is a square by doing the following:

a. Demonstrate that the quadrilateral in part A3 is a rhombus, showing and explaining all work.

b. Demonstrate that the quadrilateral in part A3 is a rectangle, showing and explaining all work. Note: Proving a right angle can be done by proving the intersecting lines are       vertical and horizontal.

4. Demonstrate that ?RKS is similar to ?SKP from part A2 by demonstrating that corresponding sides all have the same scale factor (i.e. are proportional), showing and explaining all work. B. Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized. C. Demonstrate professional communication in the content and presentation of y​‌‍‍‍‌‍‍‍‌‍‍‍‌‌‌‌‌‌‍‍​our submission.

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