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Quick Math Homework Help
Common Core Standard  G.CO.1  G.CO.4

Definition of Perpendicular Lines

  • A line is perpendicular to another line if the two lines intersect at a right angle.
  • Segment CD is perpendicular to AB because the segments create two angles of 90 degrees.





  • The slopes of Perpendicular lines are negative reciprocals. 
  • If you know the slope of one line you can determine the slope of the other line by switching the sign, and flipping the fraction. 
  • For example: If the slope of line m (the purple line) is -2 (-2/1)  then
         switch the sign to positive, and flip the fraction so the slope becomes  1/2

  • The symbol for perpendicular is ⊥

Slope of parallel lines, and perpendicular lines sample problems.

If line a || b and the slope of a = 3/5, what is the slope of line b?

3/5, the slope of parallel lines are equal.

If line a is ⊥ to line b, and line a has a slope of 1/2, what is the slope of line b?

M1=- 1/M

-2/1 the slope of perpendicular lines are negative reciprocals of one another. 
In order to create a negative reciprocal you can switch and flip, 3/5 = -5/3, 2 = -1/2


If line a || b and the slope of line a = x/8, and the slope of line 
b = (x+10)/12. What is the value of x?

Since the slopes of parallel lines are equal, set the two slopes equal to each other.
 x/8 = (x+10)/12
12x = 8x +80
4x = 80
x = 20

Find the equation of the line perpendicular to the line whose equation is 4y - 8x = 14 and whose y-intercept is +5.

Find the slope of the given line by solving for y.  
y = mx + b
4y – 8x = 14
4y = 8x + 14
y = 2x + 7/2

Now the slope of the given line is 2. 

The slope of a line perpendicular has the properties of a negative reciprocal. M1=- 1/M

Use the slope of -1/2 and a y-intercept of 5 (given) to write the equation of the new line in slope-intercept form,  
y = -1/Mx +b
y = -1/2x + 5

Find the equation of the line parallel to the line whose equation is 
y = 6x + 10 and whose y-intercept is 5.

Since the slope of the given line is 6 and the y-intercept is 5, use the formula 
y = mx + b, where m = slope and b = y-intercept.

So, the equation is:
y = 6x + 5


Perpendicular lines compared to intersecting lines

  • All perpendicular lines are intersecting lines,but not all intersecting lines are perpendicular.
  • Intersecting lines are created when two lines touch each other. 
  • Two simple examples of intersecting lines would be an (X) and a plus symbol (+)
  • Perpendicular lines are two lines that intersect at ninety degree angles.
  • A line that intersects two or more lines is a transversal. A transversal can be perpendicular to the intersected lines, but it is not mandatory.

slope parallel  lines/slope of parallel and perpendicular lines moomoomath
slope perpendicular lines
Transcript 


Hi Welcome to MooMooMath. Today we are going to take a look at some special lines. First we are going to look at the slope of parallel lines, and this symbol in black represents parallel lines. ( looks like two tall L’s) Then we have the symbol for perpendicular lines, which looks like a large upside T. What do know about parallel lines? They are lines that never intercept, and when they are on a graph they are going to have the same slope because they are going to rise and run at the same rate. So if we look at line L it has a rise of two, and a run of two. So the slope is positive 1 ( 2/2 =1) If we look at the next line it also has a slope of 1 because you count up 2 and over 2 which simplifies to 1, so the lines are the same. Let’s next look at the next graph. The line L has the same slope which is up 2 and over 2 for a slope of 1. Let’s next look at the line which is P. This time we will count down 2 and over 2 so it will be negative 2 over 2 which will be negative 1, so they have opposite slopes.  When you multiple these together (-1 and + 1) you will get a negative 1) so when you multiple two slopes together, and get negative 1 you know they are perpendicular, because the slope of perpendicular lines is the negative reciprocal. If the slope of one line is 1 over 1 you would flip it so it has a negative sign, and a slope of 1 over 1. Here is an overview of the different slopes. You have parallel which are two lines that never intercept, and you have perpendicular which have negative reciprocals so if you have a slope of ½ the perpendicular slope would be negative 2 because you flip it ( ½ becomes 2/1) and change the sign. Hope this was helpful. 
​What is a parallel line? 
Parallel lines are two lines , that no matter how far they extend, do not intersect each other. They are the same distance apart at any given point.
The slope of parallel lines are equal. 

What is a perpendicular line?
Perpendicular lines are two lines that intersect, and form right angles. Perpendicular lines have slopes that are negative reciprocals. 

Slopes of Parallel and Perpendicular Lines

Finding Slope of Parallel and Perpendicular Lines

line
  • Parallel lines never cross each other.
  • The slopes of parallel lines are equal. 
  • The rise and the run will be the same for both lines.
  • In this example both lines have a slope of 1 ( Rise=2,Run=2)
  • The symbol for parallel lines is ||
  • Parallel lines are the same distance apart from one another at any given point.
  • If two lines are parallel to a line they are parallel to each other.

Properties of Parallel Lines

railroad tracks example parallel lines real life
window example perpendicular lines real life
C
A
B
D