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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

8. Slopes of Parallel and Perpendicular Lines

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Exercise 38 Page 203

The slopes of perpendicular lines are negative reciprocals.

No, see solution.

Practice makes perfect

Lines are perpendicular if their slopes are negative reciprocals. Let's write each equation in slope-intercept form and highlight their slopes.

Given Equation	Slope-intercept form	Slope
2x-7y=-42	y= 2/7x+6	m_1= 2/7
4y=-7x-2	y= - 7/4x-1/2	m_2= - 7/4

To determine whether or not they are perpendicular, we calculate the product of the slopes. Any two slopes whose product equals - 1 are negative reciprocals, and therefore the lines are perpendicular.

m_1* m_2? =- 1

m_1= 2/7, m_2= -7/4

2/7 ( -7/4)? =- 1

Multiply fractions

- 1/2≠ - 1 *

The lines are not perpendicular.

Subchapter links

Lesson Check p.201

Practice and Problem-Solving Exercises p.201-204

Standardized Test Prep p.204

Mixed Review p.204