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8.5 Coordinate Geometry. 3 2. slope of EF =. 3 5. slope of GH =. 3 5. slope of PQ =. –2 3. 2 3. slope of CD = or –. 3 –3. slope of QR = or –1. Example 1: Finding Perpendicular and Parallel Lines. Which lines are parallel? Which lines are perpendicular?.
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8.5 Coordinate Geometry
3 2 slope of EF = 3 5 slope of GH = 3 5 slope of PQ = –2 3 2 3 slope of CD = or – 3 –3 slope of QR = or –1 Example 1: Finding Perpendicular and Parallel Lines Which lines are parallel? Which lines are perpendicular? Step 1 Find the slope of each line.
GH || PQ 3 5 3 5 The slopes are equal. = EFCD The slopes have a product of –1: • – = –1 2 3 3 2 Example 1 Continued Which lines are parallel? Which lines are perpendicular? Step 2 Compare the slopes.
–4 6 –6 4 –2 3 –3 2 slope of AB = or slope of EF = or –2 3 slope of CD = 2 3 slope of GH = 3 3 slope of JK = or 1 Check It Out! Example 2 Which lines are parallel? Which lines are perpendicular? Step 1 Find the slope of each line. A C K D E H B J G F
GHAB CD || EF –2 3 –2 3 The slopes are equal. = The slopes have a product of –1: • – = –1 3 2 2 3 Check It Out! Example 2 Continued Which lines are parallel? Which lines are perpendicular? Step 2 Compare the slopes. A C K D E H B J G F
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.
CD || BA and BC || AD Example 3: 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
TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Check It Out! Example 4 Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) 2 pairs of parallel sides, 4 right angles. parallelogram, rectangle, rhombus, square
Check It Out! Example 5 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).