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Why is this concept useful?: Perpendicular lines are two lines that intersect at a right or 90 degree angle. Everything around you, from your classroom to the piece of paper you write on form 90 degree angles. Understanding perpendicular lines help your drawers close shut properly and doors close.
Where does this concept fit into the curriculum?: Middle School

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How to identify perpendicular lines:

Perpendicular lines can be identified by their slopes. Two lines are said to be perpendicular to each other if the product of their slopes equals -1. In other words:

m_1

*

xm_2

= -1

Where

m_1

equals the slope of line 1 and

m_2

equals the slope of line 2.

For example a line with equation y = 3x + 5 has a perpendicular line with a slope of -1/3 using the formula above as 3 x -1/3 = -1

Sample Math Problems

Question

What is the slope of the line perpendicular to y =

\frac{1}{2}

x – 4?

Solution

As the slope of line 1 is ½. Our equation says that

\frac{1}{2}xm_2

= -1

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Practice Math Problems

1) Find the equation of the line through point (3,1) and is perpendicular to the line x + 5y + 5 = 0

2) What is the equation of a line perpendicular to x – 2y = 1 and passes through (1,1) is what?

3) What is the slope of a line perpendicular to a line with a slope of

-\frac{4}{5}

?

4) What is the slope of a line perpendicular to a line with a slope of 6?

Will allow us to find

m_2

. In this case

m_2

is equal to -2.

Question

What is the slope of the line perpendicular to y = -3x +10?

Solution

As the slope of line 1 is ½. Our equation says that -3

x m_2

= -1

Will allow us to find

m_2

. In this case

m_2

is equal to

\frac{1}{3}

.

Question

Find the slope of a line perpendicular to 5x + 3y+ 1 = 0

Solution

The slope of the line is 3y = -5x -1 or y =

\frac{-5}{3}(x)

-\frac{1}{3}

If

m_1

=

\frac{-5}{3}

then

m_2

will equal

Question

Find the slope of a line perpendicular to 3x – 6y = 9

Solution

The slope of the line is -6y =-3x -9 or y =

\frac{1}{2}

(x) +

\frac{3}{2}

If

m_1

= ½ then

m_2

will equal -2.

Download

\frac{3}{5}

Geometry Worksheets

Perpendicular Lines

Related Topics

Normal Distribution

Tossing a Coin

Properties of Exponents

Solve for x

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Sample Math Problems

Download FREE Math Resources

8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

Practice Math Problems