8-7+Study+Guide

    
 * Lesson 8-7**


 * Example 1 Positioning a Square**
 * Position and label a square with sides //n// units long on the coordinate plane.**

> positive //x//-axis and is on the //y//-axis. Label > the vertices //A//, //B//, //C//, and //D//. > on the //x//-axis. Since the side length is //n//, > the //x//-coordinate is //n//. > The //y//-coordinate is 0 + //n// or //n//. > 0 + //n// or //n// because the side is //n// units long.
 * Let //A//, //B//, //C//, and //D// be vertices of the square.
 * Place //A// at the origin. As a result, is on the
 * The //y//-coordinate of //B// is 0 because the vertex is
 * //D// is on the //y//-axis so the //x//-coordinate is 0.
 * The //x//-coordinate of //C// is also //n//. The //y//-coordinate is


 * Example 2 Find Missing Coordinates**
 * Name the missing coordinates for the parallelogram.**

Opposite sides of a parallelogram are congruent and parallel. So, the //y//-coordinate of //C// is //b//.

The length of is //a,// and the length of is //a//. The //x//-coordinate of //C// is //a// units more than the //x//-coordinate if //D//. So, the //x// coordinate of //C// is //a// + //c//.

The coordinates of //C// are (//c// + //a//, //b//).


 * Example 3 Coordinate Proof**
 * Given:** quadrilateral //FHJK//


 * Prove:** //FHJK// is an isosceles trapezoid

Use the Distance Formula to find the length of and. //FK// = = || //HJ// = = ||
 * Proof:**

Find the slopes of and. slope of = = or 0 || slope of = = or 0 ||

//FHJK// is an isosceles trapezoid because one set of opposite sides is parallel and the other set of opposite sides are congruent.