Describe about parallel and perpendicular lines, Mathematics

Assignment Help:

Describe about Parallel and Perpendicular Lines ?

Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect.

2217_Parallel and Perpendicular Lines.png


The blue lines are parallel. Notice that these lines have the same slope.
Two lines with the same slope are parallel.
If they had different slope then they would intersect and so they wouldn't be parallel.
If two no vertical lines are parallel, they have the same slope.
What if the lines are vertical?
If two vertical lines are parallel, they both have undefined slope.
(See example 2 for more on horizontal and vertical lines.)
Perpendicular Lines
Perpendicular lines intersect at an angle of 90 degrees, in other words they form a right angle.

28_Parallel and Perpendicular Lines 1.png


How do the slopes of these perpendicular lines compare to each other?

1301_Parallel and Perpendicular Lines 2.png


The slopes of the two perpendicular lines are 2 and -1/2. How are these slopes related? -1/2 is the negative reciprocal of 2. (See the basics section for more about negative reciprocals.)
If two lines are perpendicular, their slopes are negative reciprocals.

1752_Parallel and Perpendicular Lines 3.png

If the slopes of two lines are negative reciprocals, then the lines are perpendicular.

Example 1: What is the slope of a line that is
a. parallel to 12x - 3y = 10?
b. perpendicular to 12x - 3y = 10?
Solution: First let's find the slope of the line 12x - 3y = 10.
Put the equation in the form y = mx + b.
12x - 3y = 10
-3y = -12x +10
-3y/-3 = -12x/-3 +10/-3
Y= -4x -10/3
The slope of the line is -4.
a. All lines that are parallel to 12x - 3y = 10 have slope equal to this line. The slope of a line parallel to 12x - 3y = 10 is -4.
b. All lines that are perpendicular to 12x - 3y = 10 have slope equal to the negative reciprocal of -4. The negative reciprocal of -4 is 1/4, so the slope of a line perpendicular to 12x - 3y = 10 is 1/4.

Example 2: What is the slope of a line that is
a. parallel to the x'axis?
b. perpendicular to the x'axis?
Solution: The x'axis is a horizontal line. All horizontal lines have zero slope.
a. A line parallel to the x'axis has slope = 0.
b. A line perpendicular to the x'axis is vertical. All vertical lines have undefined slope.


Related Discussions:- Describe about parallel and perpendicular lines

What distances from the two gates should the pole, A pole has to be erected...

A pole has to be erected at a point on the boundary of a circular park of diameter 13m in such a way that the differences of its distances from two diametrically opposite fixed gat

Operation of fraction, what are the formula in the operation of fraction an...

what are the formula in the operation of fraction and how will i apply the operation of fraction on word problems

Utilizes the definition of the limit to prove the given limi, Utilizes the ...

Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero.  So, let ε 0 so that the following will be true. |x 2 - 0|

Adding fractions, please give the answer 1/9+1/3 with working out

please give the answer 1/9+1/3 with working out

What was brian''s total commission on these three sales, Brian is a real es...

Brian is a real estate agent. He forms a 2.5% commission on each sale. During the month of June he sold three houses. The houses sold for $153,000, $299,000, and $121,000. What was

Example of imaginary numbers, Example of Imaginary Numbers: Example 1...

Example of Imaginary Numbers: Example 1: Multiply √-2  and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid

Rates, we dont know how to do rates

we dont know how to do rates

Algebra 1, Im having trouble with this word problem: The three Math Idol j...

Im having trouble with this word problem: The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have be

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd