7-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation Course 3

7-5 Coordinate Geometry Warm Up Complete each sentence. Course 3 7-5 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 parallel

7-5 Coordinate Geometry Problem of the Day Course 3 7-5 Coordinate Geometry Problem of the Day What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

7-5 Learn to identify polygons in the coordinate plane. Course 3 7-5 Coordinate Geometry Learn to identify polygons in the coordinate plane.

Insert Lesson Title Here Course 3 7-5 Coordinate Geometry Insert Lesson Title Here Vocabulary slope rise run

Course 3 7-5 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.

vertical change horizontal change Course 3 7-5 Coordinate Geometry Slope is a number that describes how steep a line is. vertical change horizontal change rise run slope = =

Course 3 7-5 Coordinate Geometry The slope of a horizontal line is 0. The slope of a vertical line is undefined. When a nonzero number is divided by zero, the quotient is undefined. There is no answer. Remember!

Additional Example 1A: Finding the Slope of a Line Course 3 7-5 Coordinate Geometry Additional Example 1A: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. XY positive slope; slope of XY = = –5 –4 5 4

Additional Example 1B: Finding the Slope of a Line Course 3 7-5 Coordinate Geometry Additional Example 1B: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. ZA negative slope; slope of ZA = = – –1 2 1

Additional Example 1C: Finding the Slope of a Line Course 3 7-5 Coordinate Geometry Additional Example 1C: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. BC slope of BC is undefined

Additional Example 1D: Finding the Slope of a Line Course 3 7-5 Coordinate Geometry Additional Example 1D: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. DM slope of DM = 0

7-5 Coordinate Geometry Check It Out: Example 1A Course 3 7-5 Coordinate Geometry Check It Out: Example 1A Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A AB positive slope; slope of AB = 1 8 C E F G H D

7-5 Coordinate Geometry Check It Out: Example 1B Course 3 7-5 Coordinate Geometry Check It Out: Example 1B Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A CD slope of CD is undefined C E F G H D

7-5 Coordinate Geometry Check It Out: Example 1C Course 3 7-5 Coordinate Geometry Check It Out: Example 1C Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A EF slope of EF = 0 C E F G H D

7-5 Coordinate Geometry Check It Out: Example 1D Course 3 7-5 Coordinate Geometry Check It Out: Example 1D Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A GH negative slope; slope of GH = = – –1 3 1 C E F G H D

7-5 Coordinate Geometry Slopes of Parallel and Perpendicular Lines Course 3 7-5 Coordinate Geometry Slopes of Parallel and Perpendicular Lines Two lines with equal slopes are parallel. Two lines whose slopes have a product of –1 are perpendicular. If a line has slope , then a line perpendicular to it has slope – . Helpful Hint a b b a

Additional Example 2: Finding Perpendicular Line and Parallel Lines Course 3 7-5 Coordinate Geometry Additional Example 2: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular? slope of EF = 3 2 slope of GH = 3 5 slope of PQ = 3 5 2 3 slope of CD = or – –2 slope of QR = or –1 3 –3

Additional Example 2 Continued Course 3 7-5 Coordinate Geometry Additional Example 2 Continued Which lines are parallel? Which lines are perpendicular? GH || PQ The slopes are equal. = 3 5 EF  CD The slopes have a product of –1: • – = –1 3 2

7-5 Coordinate Geometry Check It Out: Example 2 Course 3 7-5 Coordinate Geometry Check It Out: Example 2 Which lines are parallel? Which lines are perpendicular? slope of AB = or –6 4 –3 2 slope of CD = –2 3 A slope of EF = or –4 6 –2 3 C K D E slope of GH = 2 3 H J B slope of JK = or 1 3 G F

Check It Out: Example 2 Continued Course 3 7-5 Coordinate Geometry Check It Out: Example 2 Continued Which lines are parallel? Which lines are perpendicular? CD || EF The slopes are equal. = –2 3 A C K D GH  AB E H The slopes have a product of –1: • – = –1 2 3 J B G F

Additional Example 3A: Using Coordinates to Classify Quadrilaterals Course 3 7-5 Coordinate Geometry Additional Example 3A: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A(3, –2), B(2, –1), C(4, 3), D(5, 2) CD || BA and BC || AD parallelogram

Additional Example 3B: Using Coordinates to Classify Quadrilaterals Course 3 7-5 Coordinate Geometry Additional Example 3B: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU parallelogram, rectangle, rhombus, square

7-5 Coordinate Geometry parallelogram Check It Out: Example 3A Course 3 7-5 Coordinate Geometry Check It Out: Example 3A Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) B CD || BA and BC || AD C A D parallelogram

7-5 Coordinate Geometry trapezoid Check It Out: Example 3B Course 3 7-5 Coordinate Geometry Check It Out: Example 3B Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. E(1, 5), F(7, 5), G(6, 1), H(2, 1) EF || HG E F trapezoid H G

Additional Example 4: Finding the Coordinates of a Missing Vertex Course 3 7-5 Coordinate Geometry Additional Example 4: Finding the Coordinates of a Missing Vertex Find the coordinates of the missing vertex. Rectangle WXYZ with W(–2, 2), X(3, 2), and Y(3, –4) Step 1 Graph and connect the given points. W X Step 2 Complete the figure to find the missing vertex. The coordinates of Z are (–2, –4). Y Z

Additional Example 4B: Finding the Coordinates of a Missing Vertex Course 3 7-5 Coordinate Geometry Additional Example 4B: Finding the Coordinates of a Missing Vertex Find the coordinates of the missing vertex. Rectangle JKLM with J(– 1, 2), K(4, 2), and L(4, –1) Step 1 Graph and connect the given points. J K Step 2 Complete the figure to find the missing vertex. L M The coordinates of M are (–1, –1).

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