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

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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 Course Coordinate Geometry parallel

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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 Course Coordinate Geometry

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Learn to identify polygons in the coordinate plane. Course Coordinate Geometry

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Vocabulary slope rise run Insert Lesson Title Here Course Coordinate Geometry

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Course 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.

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

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Course 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!

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Course 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 5454

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Course Coordinate Geometry 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 = = – – Additional Example 1B: Finding the Slope of a Line

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Course Coordinate Geometry 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 1C: Finding the Slope of a Line

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Course Coordinate Geometry 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 Additional Example 1D: Finding the Slope of a Line

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Course 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. AB A C B D F E H G positive slope; slope of AB = 1 8

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Course Coordinate Geometry CD slope of CD is undefined 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. A C B D F E H G

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Course Coordinate Geometry EF slope of EF = 0 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. A C B D F E H G

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Course Coordinate Geometry GH 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. A C B D F E H G negative slope; slope of GH = = – –

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Course 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 abab baba

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Course Coordinate Geometry Additional Example 2: Finding Perpendicular Line 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 – slope of CD = or – –2 3

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

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Course Coordinate Geometry Check It Out: Example 2 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

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

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Course 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) parallelogram CD || BA and BC || AD

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

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Course 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) parallelogram A C B D CD || BA and BC || AD

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

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Course 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 4: 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).

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Course 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. Additional Example 4B: Finding the Coordinates of a Missing Vertex 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).

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

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