1. 3.7 Perpendicular Lines in the Coordinate Plane This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is restricted.

2. Objectives Students will use slope to identify perpendicular lines in a coordinate plane. Students will write equations of perpendicular lines.

3. Perpendicular Lines perpendicular lines have slopes that are OPPOSITE RECIPROCALS

4. Example 6-2a Geometry The height of a trapezoid is measured on a segment that is perpendicular to a base. In trapezoid ARTP, and are bases. Can be used to measure the height of the trapezoid? Explain.

5. Example 6-2b Find the slope of each segment. Slope of

6. Example 6-2c Answer: The slope of and is 1 and the slope of is not perpendicular to and, so it cannot be used to measure height.

7. Example 6-2d The graph shows the diagonals of a rectangle. Determine whether is perpendicular to Answer: The slope of is and the slope of is Sinceis not perpendicular to

8. Example 6-3a Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of Step 1Find the slope of the given line. Original equation Subtract 7x from each side. Simplify.

9. Example 6-3b Divide each side by –2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

10. Example 6-3c Step 3Use the point-slope form to find the equation. Point-slope form and Simplify. Distributive Property

11. Example 6-3d Subtract 1 from each side. Simplify. Answer: The equation of the line is

12. Example 6-3e CheckYou can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, –1).

13. Example 6-3f Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of Answer:

14. Example 6-4a Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1Find the slope of Original equation Subtract 5x from each side. Simplify.

15. Example 6-4b Divide each side by 2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

16. Example 6-4c Step 3Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form. Point-slope form Replace x 1 with 0, y 1 with 6, and m with Distributive Property Answer: The equation of the line is

17. Example 6-4d Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through the x -intercept of that line. Answer: