Related Topics:

Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Student Outcomes

- Students generalize the criterion for perpendicularity of two segments that meet at a point to any two segments in the Cartesian plane.
- Students apply the criterion to determine if two segments are perpendicular.

**Segments That Meet at Right Angles**

Classwork

**Opening Exercise**

Carlos thinks that the segment having endpoints π΄(0,0) and π΅(6,0) is perpendicular to the segment with endpoints
π΄(0,0) and πΆ(β2,0). Do you agree? Why or why not?

Working with a partner, given π΄(0,0) and π΅(3,β2), find the coordinates of a point πΆ so that π΄πΆ β₯ π΄π΅.

**Example**

Given points π΄(2,2), π΅(10,16), πΆ(β3,1), and π·(4,β3), are π΄π΅ and πΆπ· perpendicular? Are the lines containing the segments perpendicular? Explain.

**Exercises**

- Given π΄(π1, π2), π΅(π1, π2), πΆ(π1, π2), and π·(π1, π2), find a general formula in terms of π1, π2, π1, π2, π1, π2, π1, and π2 that will let us determine whether π΄π΅ and πΆπ· are perpendicular.
- Recall the Opening Exercise of Lesson 4 in which a robot is traveling along a linear path given by the equation π¦ = 3π₯ β 600. The robot hears a ping from a homing beacon when it reaches the point πΉ(400,600) and turns to
travel along a linear path given by the equation π¦ β 600 = β1/3(π₯ β 400). If the homing beacon lies on the π₯-axis,
what is its exact location? (Use your own graph paper to visualize the scenario.)

a. If point πΈ is the π¦-intercept of the original equation, what are the coordinates of point πΈ?

b. What are the endpoints of the original segment of motion?

c. If the beacon lies on the π₯-axis, what is the π¦-value of this point, πΊ?

d. Translate point πΉ to the origin. What are the coordinates of πΈβ², πΉβ², and πΊβ²?

e. Use the formula derived in this lesson to determine the coordinates of point πΊ - A triangle in the coordinate plane has vertices π΄(0,10), π΅(β8,8), and πΆ(β3,5). Is it a right triangle? If so, at which vertex is the right angle? (Hint: Plot the points, and draw the triangle on a coordinate plane to help you determine which vertex is the best candidate for the right angle.)
- π΄(β7,1), π΅(β1,3), πΆ(5,β5), and π·(β5,β5) are vertices of a quadrilateral. If π΄πΆ bisects π΅π·, but π΅π· does not bisect π΄πΆ, determine whether π΄π΅πΆπ· is a kite.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.