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Parallel and Perpendicular
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Now that you learned about parallel lines, it is now time to continue your journey and look at perpendicular lines! Perpendicular lines are pretty cool because they sort of look like a cross. So, yes to answer your question, (if you were asking it) perpendicular lines do indeed cross and touch and all that jazz. They can be thought of the opposite of parallel lines, in a way.
Perpendicular lines have to touch and meet at a 90 degree angle. They create right angles, which are 90 degree angles. Also, the equations and graphing of perpendicular lines work differently from that of parallel lines. Instead of having the same slope for the equations in order for them to be parallel, you actually want a different slope. Well, not a completely different slope, not one you make up. For example, you wouldn't go from a slope of 4 to a slope of 13 and call it perpendicular. The slope has to be the negative reciprocal of the original equation. This means, that for example, if you have a slope of 2 and you want to find the negative reciprocal of that slope, then it would be -1/2. In order to find the negative reciprocal, you can basically just flip the original equation and put a negative sign in front of it. For example, a slope of -3 would turn int this is so STUPID
Here are some examples of perpendicular lines:
Remember this information! It's important!
Perpendicular lines are also used in real life.
This is an example of equations and their negative reciprocals.
What is the equations of the line that is perpendicular to the line of Y=7x+3?
-The first thing to do is make sure the equation is in slope-intercept form, Y=mx+b
-The equation is in the right form. Lucky for us! So we don't have to change anything.
-Then, find the slope of the equation, which would be 7.
-The line to intersect to make perpendicular line has to have a negative reciprocal slope.
-So to find the reciprocal of any number, all you have to do is put it into fraction form and switch the numerator and denominator. So the reciprocal of X would be 1/X.
-So the reciprocal of 7 is 1/7.
-And you also have to make the reciprocal a negative. So if the slope is positive, now it will be negative; if it was negative before, now it is positive.
-So the new slope is -1/7.
Another example of lines that are perpendicular are
The slopes define everything because they are negative reciprocals.
Graphing perpendicular lines are also very very easy.
If you want to graph perpendicular lines, or check to see if two lines are perpendicular, all you need to do is follow these easy steps.
-As with parallel lines, the first thing you should do is make sure the equations are all in slope-intercept form.
-Then, graph them regularly, starting with the y-intercept and measuring out the slope and everything.
-If you just wanted to check if two lines were perpendicular, you don't really need to graph it, unless you don't trust yourself and want to double check. Always good.
-Because all you need is the slope and they only have to be negative reciprocals.
-But if you graphed them anyways just for fun :), you can check them with a protractor if you really really want to see if the lines form four right angles, that are 90 degrees when they intersect.
-So as you can see, graphing perpendicular equations are always fun and simple.
Perpendicular lines are cool, WANT TO KNOW WHY?! Of course you do! Well, first off, they can intersect, so do not freak out if your lines are touching and make a 90 degree angle! That's what these lines are supposed to do! Basically, just remember the main things about these lines: they can touch, make a 90 degree angle and have slopes of negative reciprocals.
Parallel and Perpendicular Lines in a nutshell
Parallel lines are the same distance apart and will never cross.
Perpendicular lines intersect to form four right angles.
And to see if two equations are parallel, all you need are matching slopes.
And to see if two equations are perpendicular, all you need are negative reciprocal slopes.
SO REMEMBER, IT'S ALL ABOUT THE SLOPES!
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