Pre-Algebra 5.5 Coordinate Geometry
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 Warm Up
Learn to identify polygons in the coordinate plane.
slope rise run Vocabulary
Slope is a number that describes how steep a line is.
The slope of a horizontal line is 0. The slope of a vertical line is undefined. slope = vertical change horizontal change = rise run
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A. XY positive slope; slope of XY = = –5 – Example: 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. B. ZA negative slope; slope of ZA = = – – Example: 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. C. BC slope of BC is undefined Example: 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. D. DM slope of DM = 0 Example: 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. A. AB A C B D F E H G positive slope; slope of AB = 1 8 Try This
B. CD slope of CD is undefined 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 Try This
C. EF slope of EF = 0 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 Try This
D. GH 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 = = – – Try This
Slopes of Parallel and Perpendicular Lines Two lines with equal slopes are parallel. Two lines whose slopes have a product of –1 are perpendicular.
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 Example: Finding Perpendicular Line and Parallel Lines
The slopes are equal. = The slopes have a product of –1: – = – GH || PQ EF CD Which lines are parallel? Which lines are perpendicular? Example Continued
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 Try This
CD || EF GH AB A C B D F E K J H G Which lines are parallel? Which lines are perpendicular? The slopes are equal. = –2 3 –2 3 The slopes have a product of –1: – = – Try This
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram CD || BA and BC || AD Example: Using Coordinates to Classify Quadrilaterals
B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) parallelogram, rectangle, rhombus, square 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 Example: Using Coordinates to Classify Quadrilaterals
C. G(1, –1), H(1, –2), I(3, –3), J(3, 1) trapezoid Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. GH || JI Example: Using Coordinates to Classify Quadrilaterals
D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) parallelogram, rectangle Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. WZ || XY and WX || ZY WZZY, ZYXY, XYWX and WXWZ Example: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) parallelogram A C B D CD || BA and BC || AD Try This
B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) trapezoid E F H G EF || HG Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) parallelogram, rectangle, rhombus, square X W Y Z ZW || YX and WX || ZY WXZW, XYWX, YZXY and ZWYZ Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) parallelogram, rectangle R S U T TU || SR and ST || RU TURU, RURS, RSST and STTU Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? – 10 3 MN, RQ Lesson Quiz
D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) parallelogram, rectangle Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. WZ || XY and WX || ZY WZZY, ZYXY, XYWX and WXWZ Example: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) parallelogram A C B D CD || BA and BC || AD Try This
B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) trapezoid E F H G EF || HG Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) parallelogram, rectangle, rhombus, square X W Y Z ZW || YX and WX || ZY WXZW, XYWX, YZXY and ZWYZ Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) parallelogram, rectangle R S U T TU || SR and ST || RU TURU, RURS, RSST and STTU Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. Try This
Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? – 10 3 MN, RQ Lesson Quiz