# Equations for Lines Using Normal Segments

### New York State Common Core Math Geometry, Module 4, Lesson 7

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 a1x + a2y + c, recognizing the segments from (0,0) to (a1, a2) as a normal and - a2/a1 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.

1. 6𝑥 +3𝑦 = 12
2. 5𝑥 +7𝑦 = 14
3. 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

1. 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.
2. 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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