1. 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.

2. Vocabulary equidistant

3. Concept

7. Example 3 Distance Between Parallel Lines Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, 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. From their equations, we know that the slope of line a and line b is 2. Sketch line p through the y-intercept of line b, (0, –1), perpendicular to lines a and b. a b p

8. Example 3 Distance Between Parallel Lines Step 1 Use the y-intercept of line b, (0, –1), as one of the endpoints of the perpendicular segment. Write an equation for line p. The slope of p is the opposite reciprocal of Point-slope form Simplify. Subtract 1 from each side.

9. Example 3 Distance Between Parallel Lines Use a system of equations to determine the point of intersection of the lines a and p. Step 2 Substitute 2x + 3 for y in the second equation. Group like terms on each side.

10. Example 3 Distance Between Parallel Lines Simplify on each side. Multiply each side by. Substitutefor x in the equation for p.

11. Example 3 Distance Between Parallel Lines Simplify. The point of intersection is or (–1.6, –0.2).

12. Example 3 Distance Between Parallel Lines Use the Distance Formula to determine the distance between (0, –1) and (–1.6, –0.2). Step 3 Distance Formula x 2 = –1.6, x 1 = 0, y 2 = –0.2, y 1 = –1 Answer: The distance between the lines is about 1.79 units.

13. Example 3 A.2.13 units B.3.16 units C.2.85 units D.3 units Find the distance between the parallel lines a and b whose equations are and, respectively.