1. Holt CA Course 1 8-5 Coordinate Geometry Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 8-5 Coordinate Geometry Warm Up Complete each sentence. 1. Two lines in a plane that never meet are called lines. 2. lines intersect at right angles. 3. The symbol || means that lines are. 4. When a transversal intersects two lines, all of the acute angles are congruent. parallel Perpendicular parallel

3. Holt CA Course 1 8-5 Coordinate Geometry MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. Also covered: AF3.3 California Standards

4. Holt CA Course 1 8-5 Coordinate Geometry Vocabulary polygon quadrilateral trapezoid parallelogram rectangle rhombus square

5. Holt CA Course 1 8-5 Coordinate Geometry In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

6. Holt CA Course 1 8-5 Coordinate Geometry Slopes of Parallel and Perpendicular Lines Any two nonvertical lines with equal slopes are parallel. Any two vertical lines are parallel. Any two nonvertical lines whose slope have a product of –1 are perpendicular. Vertical and horizontal lines are perpendicular.

7. Holt CA Course 1 8-5 Coordinate Geometry Additional Example 1: Finding Perpendicular and Parallel Lines Which lines are parallel? Which lines are perpendicular? slope of EF = 3232 slope of GH = 3535 slope of PQ = 3535 slope of QR = or –1 3 –3 2323 slope of CD = or – –2 3 Step 1 Find the slope of each line.

8. Holt CA Course 1 8-5 Coordinate Geometry Additional Example 1 Continued The slopes are equal. = 3535 3535 The slopes have a product of –1: – = –1 3232 2323 GH || PQ EF  CD Which lines are parallel? Which lines are perpendicular? Step 2 Compare the slopes.

9. Holt CA Course 1 8-5 Coordinate Geometry Check It Out! Example 1 A C B D F E K J H G Which lines are parallel? Which lines are perpendicular? slope of AB = or –6 4 –3 2 slope of CD = –2 3 slope of EF = or –4 6 –2 3 slope of GH = 2323 slope of JK = or 1 3 Step 1 Find the slope of each line.

10. Holt CA Course 1 8-5 Coordinate Geometry CD || EF GH  AB A C B D F E K J H G Check It Out! Example 1 Continued Which lines are parallel? Which lines are perpendicular? The slopes are equal. = –2 3 –2 3 The slopes have a product of –1: – = –1 2323 3232 Step 2 Compare the slopes.

11. Holt CA Course 1 8-5 Coordinate Geometry A polygon is a closed plane figure formed by three or more line segments called sides. Each side meets exactly two other sides, one on each end, in a common endpoint. Quadrilaterals are polygons with four sides and four angles. Quadrilaterals with certain properties are given additional names.

12. Holt CA Course 1 8-5 Coordinate Geometry

13. Holt CA Course 1 8-5 Coordinate Geometry Additional Example 2: Using Coordinates to Classify Quadrilaterals Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram CD || BA and BC || AD

14. Holt CA Course 1 8-5 Coordinate Geometry R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) parallelogram, rectangle, rhombus, square Check It Out! Example 2 Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral. TU || SR and ST || RU TURU, RURS, RSST and STTU 2 pairs of parallel sides, 4 right angles.

15. Holt CA Course 1 8-5 Coordinate Geometry Rectangle WXYZ with W(–2, 2), X(3, 2), and Y(3, –4) Step 2 Complete the figure to find the missing vertex. Additional Example 3: Finding the Coordinates of a Missing Vertex Find the coordinates of the missing vertex. W Y X Z Step 1 Graph and connect the given points. The coordinates of Z are (–2, –4).

16. Holt CA Course 1 8-5 Coordinate Geometry Rectangle JKLM with J(– 1, 2), K(4, 2), and L(4, –1) Step 2 Complete the figure to find the missing vertex. Check It Out! Example 3 Find the coordinates of the missing vertex. J L K M Step 1 Graph and connect the given points. The coordinates of M are (–1, –1).

17. Holt CA Course 1 8-5 Coordinate Geometry Lesson Quiz Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? 1 8 7 – 10 3 MN, RQ