1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 3–5) CCSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate 3.6: Perpendicular Postulate Example 1:Real-World Example: Construct Distance From Point to a Line Example 2:Distance from a Point to a Line on Coordinate Plane Key Concept: Distance Between Parallel Lines Theorem 3.9: Two Line Equidistant from a Third Example 3:Distance Between Parallel Lines

3. CCSS Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 2 Reason abstractly and quantitatively. 4 Model with mathematics.

4. Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel lines.

5. Vocabulary equidistant

6. Concept

8. Example 1 A.AD B.AB C.CX D.AX KITES Which segment represents the shortest distance from point A to DB?

9. Step 1Find the slope of line s. Begin by finding the slope of the line through points (0, 0) and (–5, 5). COORDINATE GEOMETRY 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)

10. Example 2 Distance from a Point to a Line on Coordinate Plane Then write the equation of this line by using the point (0, 0) on the line. Slope-intercept form m = –1, (x 1, y 1 ) = (0, 0) Simplify. The equation of line s is y = –x.

11. Example 2 Distance from a Point to a Line on Coordinate Plane Step 2Write an equation of the line t perpendicular to line s through V(1, 5). Since the slope of line s is –1, the slope of line t is 1. Write the equation for line t through V(1, 5) with a slope of 1. Slope-intercept form m = 1, (x 1, y 1 ) = (1, 5) Simplify. The equation of line t is y = x + 4. Subtract 1 from each side.

12. Example 2 Distance from a Point to a Line on Coordinate Plane Step 3Use the Distance Formula to determine the distance between Z(–2, 2) and V(1, 5). Distance formula Substitution Simplify. Answer:The distance between the point and the line is or about 4.24 units.

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

14. Concept

16. End of the Lesson