1. Splash Screen

2. Concept Label your diagram with the following new points: D E F G

3. Concept

4. In other words, if you have a line, a and have a point not on the line, W then there is only one line that exists that is perpendicular to the original line that goes through the point.

5. Example 1 Construct Distance From Point to a Line A. A certain roof truss is designed so that the center post extends from the peak of the roof (point A) to the main beam. Construct and name the segment whose length represents the shortest length of wood that will be needed to connect the peak of the roof to the main beam. A Main Beam X

6. Example 1 B. Which segment represents the shortest distance from point A to DB?

7. Extra Examples A B C A B C D E

8. End of the Lesson

9. Concept By definition, parallel lines do not intersect. An alternate definition states that two lines in a plane are parallel if they are everywhere equidistant. Equidistant means that the distance between two lines measured along a perpendicular line to the lines is always the same. This leads to the definition of the distance between two parallel lines.

10. Example 1 Find the distance between each pair of parallel lines with the given equations. 2 a) y = 2 y = 3 b) x = 9 x = 1 c) y = -5 y = 7 d) x = 4 x = -6

11. COORDINATE GEOMETRY A. Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5). Example 2 Distance from a Point to a Line on Coordinate Plane (–5, 5) (0, 0) V(1, 5)

12. Example 2 COORDINATE GEOMETRY B. Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1).

13. Concept

14. Example 3 Distance Between Parallel Lines A. Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively. b a p

15. Example 3 B. Find the distance between the parallel lines a and b whose equations are and, respectively.