Geometry/Trig Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector

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1 Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector Learning Goals: #14: How do I write the equation of a perpendicular bisector? Warm-up What is the equation of a line that passes through (-1,-2) and is perpendicular to -5x = 6y + 18? Sketch the perpendicular bisector of segment AB: What are the two properties that we need in order to write the equation of a perpendicular bisector? Take a look at the following question: Write an equation of the line that is perpendicular to the line that contains the points A( 4,2) and B(8,6) and passes through the midpoint of AB. Don t solve it yet! Answer the following questions! 1. How is this question different from the do now? 2. Since the new line is perpendicular to the given and passes through the midpoint, what can we call this line?

2 Jot it down! What information do you need to know in order to write the equation of a line in point-slope form? To write the equation of the perpendicular bisector of a segment: Property 1: Property 2: Substitute into y y 1 = m(x x 1 ) Now, Now, Let s let s try one! Write the equation of the perpendicular bisector of segment A(1,4) and B(5,6). Substitute b. We know that we wrote the equation of the perpendicular bisector, because - its slope is the slope of AB and - The line travels through the of AB. c. Graph the perpendicular bisector, and the line Segment AB. Does it appear to satisfy the properties of a perpendicular bisector? Why or why not?

3 ACRONYM TO REMEMBER THE STEPS FOR PERPENDICULAR BISECTOR: Practice: 1. Write the equation of the perpendicular bisector of segment MR, where M is (-6, 6) and R is (2, -2). Step 1 (M): Step 3 (P) Step 2 (S): Step 4 (P): a. Justify your answer: I know that this is the equation of the perpendicular bisector, because - its slope is the slope of MR and - The line travels through the of AB. 2. Line segment JK, has point J(-4, 5) and K(-2, 9). Find the equation of the perpendicular bisector of JK. a. Justify your answer.

4 3. In circle O, a diameter has endpoints A( 5,4) and B(3, 6). What are the coordinates of the center of the circle? a. Find the equation of the line that would make a perpendicular diameter AB. Step 1 (M): Step 3 (P) Step 2 (S): Step 4 (P): 4. Line segment BD has the point B (-3, 4) and B (5, 8). Find the equation of the perpendicular bisector of BD. 5. Write the equation of the perpendicular bisector of segment AB, where A is (-5, 6) and B is (2, -4).

5 6. Use parts a through c to justify that the line y 1 = 3 (x 2) is the perpendicular bisector of AB. 4 a. How is this question different than what we learned above? b. If this line is the perpendicular bisector, then what must be true about the slopes of the lines? c. Is this true in this case? (hint: find the slope of both) d. If this line is the perpendicular bisector, then what must be true about the point used in the equation? Is this true in this case? (hint: find the midpoint of AB) Conclusion: Is the line y 1 = 3 (x 2) is the perpendicular bisector of AB? Justify your answer using 4 complete sentences.

6 Name: Date: Lesson 1-11: Homework 1. Line segment GH has endpoints G(5, -2) and H. The midpoint is M(-10, 1). What are the coordinates of endpoint H? 2. Line segment AB has endpoints A( 2, 3) and ( 4,6) B. What is the perpendicular bisector AB? 3. Write the equation of the perpendicular bisector of line segment AB, if A(3, 10) and B( 4, 3)?