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Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button or press the Space Bar to display the answers. Lesson 3-1 Parallel Lines and Transversals Lesson 3-2 Angles and Parallel Lines Lesson 3-3 Slopes of Lines Lesson 3-4 Equations of Lines Lesson 3-5 Proving Lines Parallel Lesson 3-6 Perpendiculars and Distance Example 1 Distance from a Point to a Line Example 2 Construct a Perpendicular Segment Example 3 Distance Between Lines OBJECTIVE: To find the distance between a point and a line and between parallel lines (2.9.8E) (M8.C.1) Draw the segment that represents the distance from Answer: Since the distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point, Draw the segment that represents the distance from Answer: Construct a line perpendicular to line s through V(1, 5) not on s. Then find the distance from V to s. Graph line s and point V. Place the compass point at point V. Make the setting wide enough so that when an arc is drawn, it intersects s in two places. Label these points of intersection A and B. Put the compass at point A and draw an arc below line s. (Hint: Any compass setting greater than will work.) Using the same compass setting, put the compass at point B and draw an arc to intersect the one drawn in step 2. Label the point of intersection Q. Draw . and s. Use the slopes of lines are perpendicular. and s to verify that the The segment constructed from point V(1, 5) perpendicular to the line s, appears to intersect line s at R(–2, 2). Use the Distance Formula to find the distance between point V and line s. Answer: The distance between V and s is about 4.24 units. Construct a line perpendicular to line m through Q(–4, –1) not on m. Then find the distance from Q to m. Answer: Find the distance between the parallel lines a and b whose equations are and respectively. 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. First, write an equation of a line p perpendicular to a and b. The slope of p is the opposite reciprocal of 2, Use the y-intercept of line a, (0, 3), as one of the endpoints of the perpendicular segment. Point-slope form Simplify. Add 3 to each side. Next, use a system of equations to determine the point of intersection of line b and p. Substitute 2x–3 for y in the second equation. Group like terms on each side. Simplify on each side. Substitute 2.4 for x in the equation for p. The point of intersection is (2.4, 1.8). Then, use the Distance Formula to determine the distance between (0, 3) and (2.4, 1.8). Distance Formula Answer: The distance between the lines is 2.7 units. or about Find the distance between the parallel lines a and b whose equations are respectively. Answer: and End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.