body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

8. Slopes of Parallel and Perpendicular Lines

Continue to next subchapter

Exercise 36 Page 203

The slopes of the perpendicular lines are negative reciprocals.

Yes, see solution.

Practice makes perfect

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

Given Equation	Slope-intercept form	Slope
y=- x-7	y= - 1x-7	m_1= - 1
y-x=20	y= 1x+20	m_2= 1

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 will be perpendicular.

m_1* m_2? =- 1

m_1= - 1, m_2= 1

-1 ( 1)? =- 1

Identity Property of Multiplication

-1 = - 1 ✓

The slopes of the given lines are negative reciprocals, so the lines are perpendicular.

Subchapter links

Lesson Check p.201

Practice and Problem-Solving Exercises p.201-204

Standardized Test Prep p.204

Mixed Review p.204