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Focus Do not follow where the path may lead. Go instead where there is no path and leave a trail. -- Ralph Waldo Emerson Perpendiculars and Distance Chapter 3 Section 6 Find the Distance between: A point and a line, 2 parallel lines Distance, point and a line Draw the shortest distance between line q and M point M q You Draw Distance Draw a segment that represents the distance from point P to AB. P A B Draw a segment that represents the distance from point Q to RS. S Q R Distance Distance on the coordinate plane always involves 2 points. Distance between. . . 1) 2 points 2) point and a line 3) 2 lines Distance from a point to a line t Construct a line perpendicular to line s through V(1, 5) not on s. Then find the distance from V to s. 1. What do we know about perpendicular Lines? slopes are “twice opposite” 2. Find the slope of line s then our new slope ms = 1, mt = -1 ?? Distance from a point to a line t 3. Find the Distance between the point and the line. Note: Line t appears to intersect line s at (-2, 2) Distance Between Parallel Lines M 2.5 cm s q Distance between 2 lines Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x –3 You will need to solve a system of equations to find the endpoints of a segment that is perpendicular to both a and b. The slope of lines a and b is 2. y = 2x + 3 and y = 2x –3 1. Wisely choose any point (0, 3) on the line 2. Slope of line p ? mp = -1/2 3. What do we know? point and slope Point-slope form Simplify. Add 3 to each side. What do we need for Distance? What do we have now? p a b y = 2x + 3 y = 2x – 3 p and a intersect at (0, 3) p and b intersect at ??? Find the intersection and we can plug it into our formula Find the intersection of 2 lines Where do they intersect? At the point they share Group like terms on each side. Simplify on each side. Divide each side by . Substitute 2.4 for x in the equation for p. The point of intersection is (2.4, 1.8). What do we have now? Our 2 points for distance formula (0, 3) Distance Formula x2 = 2.4, x1 = 0, y2 = 1.8, y1 = 3 (2.4, 1.8) Distance and Parallel Lines Find the distance between the parallel lines a and b whose equations are and 2.85 units Theorum 3.9 Homework p. 185-186 #5-10, 12-18(evens) 22, 29-31 (15 problems)