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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 4, Lesson 7

Student Outcomes

- Students state the relationship between previously used formats for equations for lines and the new format a
_{1}x + a_{2}y + c, recognizing the segments from (0,0) to (a_{1}, a_{2}) as a normal and - a_{2}/a_{1}as a slope. - Students solve problems that are dependent upon making such interpretations.

**Equations for Lines Using Normal Segments**

Classwork

**Opening Exercise**

The equations given are in standard form. Put each equation in slope-intercept form. State the slope and the 𝑦-intercept.

- 6𝑥 +3𝑦 = 12
- 5𝑥 +7𝑦 = 14
- 2𝑥 −5𝑦 = −7

**Example**

Given 𝐴(5,−7) and 𝐵(8,2):

a. Find an equation for the line through 𝐴 and perpendicular to 𝐴𝐵

b. Find an equation for the line through 𝐵 and perpendicular to 𝐴𝐵

**Exercises**

- Given 𝑈(−4,−1) and 𝑉(7,1):

a. Write an equation for the line through 𝑈 and perpendicular to 𝑈𝑉.

b. Write an equation for the line through 𝑉 and perpendicular to 𝑈𝑉. - Given 𝑆(5,−4) and 𝑇(−8,12):

a. Write an equation for the line through 𝑆 and perpendicular to 𝑆𝑇.

b. Write an equation for the line through 𝑇 and perpendicular to 𝑆𝑇.

**Closing**

Describe the characteristics of a normal segment.

Every equation of a line through a given point (𝑎, 𝑏) has the form 𝐴(𝑥 −𝑎) + 𝐵(𝑦 − 𝑏) = 0. Explain how the values of
𝐴 and 𝐵 are obtained.

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