VERY SIMPLE Coordinate Geometry

[BL4CKCR4Y0NS]

Homework Statement

Using the concept of equal slopes, state whether the following sets of points are collinear or not
A(5, -6) B(0, -1) C(-4, 3)

Homework Equations

Slope = vertical rise/horizontal run

The Attempt at a Solution

I only got as far as...
5-0/-6+1 = 5/-5
I think what I just did was already incorrect. I actually have a few of these questions but I'm sure that if someone points me in the right direction with this one, I can figure out the rest.

Thanks in advance. (yes, I know this is very basic maths)

 

[HallsofIvy]

I only got as far as 5-0/-6+1= 5/-5

First, please use parentheses. What you wrote is really 5- 0+ 1= 6! You mean, of course, (5-0)/(-6+1)= 5/(-5)= -1.

But also important is to say why you are doing calculations. I think you trying to do is calculate the slope of the line from (5, -6) to (0, -1). And yes, you are doing it wrong. Slope is defined as "change in y divided by change in x". Going from (0, -1) to (5, -6), y changes from -1 to -6 so the change is -6-(-1)= -5 and that is the numerator of the fraction. x changes from 0 to 5 so the change is 5- 0= 5 and that is the denominator of the fraction. The slope is (-5)/5= -1. (That is the same as before but only because this is a special case.)

Now, what is the slope of the line from (0, -1) to (-4, 3)? What does that tell you?

 

[tiny-tim]

Hi BL4CKCR4Y0NS!

Using the concept of equal slopes, state whether the following sets of points are collinear or not
A(5, -6) B(0, -1) C(-4, 3)
…

5-0/-6+1 = 5/-5
I think what I just did was already incorrect.

No, it's fine … the slope is -1.

Now do B and C the same way.

(remember, if you want to check your answer, you can easily draw it on a graph! )

 

[snshusat161]

First you have to think, how you can use slope's to find out that lines are collinear. You have the concept that two lines are parallel, if they have their slope equal, now find out the slope of the line AB and BC, if you'll get the slope equal that means that AB and BC are parallel lines, but are they really parallel? They have 'B' point common, so they are not parallel lines, so only thing we can say about it is that they are collinear means AB and BC are the same line. Now to find the slope you have to use equation, $$\frac{y_2 - y_1}{x_2 - x_1}$$

 

[snshusat161]

I messed up with latex code, so can anybody here can correct it.

 

[HallsofIvy]

Hi BL4CKCR4Y0NS!


No, it's fine … the slope is -1.

Yes, but only because 1/(-1)= -1. He actually calculated the reciprocal of the slope.

Now do B and C the same way.

(remember, if you want to check your answer, you can easily draw it on a graph! )

 

[snshusat161]

Thanks HallsofIvy for correcting my latex code. I know that it isn't a right place to ask this question but I can't find any better place to ask. Can you give me the link to the page where the instructions to properly write latex code is given. I've seen it once but now I've lost that link and unable to find it using search functionality.

 

[tiny-tim]

Yes, but only because 1/(-1)= -1. He actually calculated the reciprocal of the slope.

ah, but the question didn't ask for the slope …

so long as he uses the same method for each line, the procedure is perfectly valid

(and snshusat161, a good place to start is http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000" )

 

[BL4CKCR4Y0NS]

Hi BL4CKCR4Y0NS!


No, it's fine … the slope is -1.

Now do B and C the same way.

(remember, if you want to check your answer, you can easily draw it on a graph! )

I did what tiny-tim said, and I ended up with 5/(-4)
But I'm not sure if I'm correct. What I did was (just in case I got it wrong and you needed working out to see where I went wrong)

5/(-5) = 1/-1
(1+4)/(-1)-3
= 5/(-4)

Thanks for all the replies guys... I appreciate it. =]

 

[snshusat161]

What did you mean by 5/-4. Is it collinear or not. What i told earlier use it.

 

[BL4CKCR4Y0NS]

Okay, I did as you said and...
A and B came back with -1
B and C came back with -1

I'm not sure what I am supposed to tell from that ... does "-1" on both mean that they are collinear?

 

[snshusat161]

no, it means that both are parallel but do you ever heard parallel lines intersecting at any point, therefore both lines AB and BC are not parallel but the same line and since points A, B and C lies on the same line they are collinear.

And "-1" doesn't mean that they are collinear. Any number will do well if you get it for both AB and BC.

 

[tiny-tim]

Okay, I did as you said and...
A and B came back with -1
B and C came back with -1

I'm not sure what I am supposed to tell from that ... does "-1" on both mean that they are collinear?

Yes, "-1" on both means they have the same slope, and since they also share a point, they must be on the same line.

(incidentally, of course, if you check A and C, you should find the same )

 

[BL4CKCR4Y0NS]

Thanks tiny-tim =D
I didn't actually understand snshusat161's last post and was a little afraid to ask again because I'm so intellectually inferior and probably seem annoying... >_>

Thanks again guys. I got the rest of the questions =D

 

[snshusat161]

I didn't actually understand snshusat161's last post and was a little afraid to ask again because I'm so intellectually inferior and probably seem annoying... >_>

I wanted to clarify in my last post that equal slope doesn't mean that two lines are collinear but if they have some common point then they are collinear.

 

[snshusat161]

Or simply use this equation:

$$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$ = $$\frac{y_{3} - y_{2}}{x_{3} - x_{2}}$$

 

[Mentallic]

There's no point in using the equation if the OP doesn't understand how and why it's being used.

 

[BL4CKCR4Y0NS]

So the common point in this case would be the "-1" ?

 

[snshusat161]

No, I think you are totally confused and you don't know how we represent any point in coordinate geometry. Let me search some good tutorial page for you.

 

[Mentallic]

You need to go back and study coordinate geometry from the very start.
Simply put, as snshusat161 has said, you seem to be complete oblivious as to how coordinate geometry works and putting this added pressure of trying to solve problems is completely pointless to you.

 

[snshusat161]

You need to go back and study coordinate geometry from the very start.
Simply put, as snshusat161 has said, you seem to be complete oblivious as to how coordinate geometry works and putting this added pressure of trying to solve problems is completely pointless to you.

Now a day a huge percent of students used to mug up the formula's and the step by step way to solve the problem and can clear most of the portion of their syllabus successfully but coordinate geometry and trigonometry require special thinking ability to solve and that's the reason why such problem arises.

here's no point in using the equation if the OP doesn't understand how and why it's being used.

Some student may be happy to use it without any understanding.

 

[tiny-tim]

So the common point in this case would be the "-1" ?

Sorry, I'm not understanding you.

The concept of equal slopes means that the slope of the line AB has to be the same as the slope of the line BC.

In this case, it's -1.

(or were you making some other point?)

 

[snshusat161]

Sorry, I'm not understanding you.

The concept of equal slopes means that the slope of the line AB has to be the same as the slope of the line BC.

In this case, it's -1.

(or were you making some other point?)

Question is to prove that points are collinear using equal slope concept. But that guy don't know what do the term "Slope" mean, neither he know what is "point".
He has already proved that both of that line has a equal slope that is equal to "-1". But he only knew that he has to use formula of difference in ordinates divided by difference in abscissa. He don't know what are A(5, -6) B(0, -1) C(-4, 3). If one has said AB and BC so what does it mean, so nobody can make him understand.

 

[tiny-tim]

… But that guy don't know what do the term "Slope" mean, neither he know what is "point". …

snshusat161, referring to another PF member as "that guy" is neither friendly nor even polite.

And please don't presume to answer for BL4CKCR4Y0NS as if he isn't here.

Some of your previous posts have been less than helpful. In particular, BL4CKCR4Y0NS did not understand the following, and I'm not sure I do …

no, it means that both are parallel but do you ever heard parallel lines intersecting at any point, therefore both lines AB and BC are not parallel but the same line and since points A, B and C lies on the same line they are collinear.

 

[snshusat161]

Some of your previous posts have been less than helpful. In particular, BL4CKCR4Y0NS did not understand the following, and I'm not sure I do

cause I'm not good in english

 

[snshusat161]

snshusat161, referring to another PF member as "that guy" is neither friendly nor even polite.

lol, can't you see how difficult is to write his username.

And please don't presume to answer for BL4CKCR4Y0NS

I don't have any personal issuse's with BL4CKCR4Y0NS. I just want to say that what the need to explain him if he already got his solution. Since he don't know the basic concept every explanation will go above his head.

 

[Mentallic]

tiny-tim, but it also seems to me like you're taking a stab at snshusat161's English skills. His post makes sense (and it's very clear to me what he's trying to say), so I find it hard to believe that you didn't understand what he was saying, especially since you basically repeated what he was trying to say in the very next post:

Yes, "-1" on both means they have the same slope, and since they also share a point, they must be on the same line.

And I agree with snshusat161 that blackcrayons doesn't understand coordinate geometry whatsoever. This post:

So the common point in this case would be the "-1" ?

is obviously telling us that he thinks the -1 is representing a point. What is this telling you about blackcrayons' abilities in this topic?

Go back and study coordinate geometry from the beginning

 

[BL4CKCR4Y0NS]

This is actually the beginning ... there is no bit in the booklet that says anything else and believe me, I have read through it multiple times.

And just for the record, the booklet is called "Coordinate geometry (I)"

 

[snshusat161]

When we say 'point' in Coordinate Geometry then we mean a very specific position in plane (in 2D) and in space (in 3D). Think of it in this way. If i'll say 10 cm away from left margin of your notebook. Where you will point? And if i'll also add that 5 cm from top margin then you can easily show that particular point.

 

[snshusat161]

if you get any problem in understanding, tell me, I'll try to explain it cause you can't understand anything until you learn those basic and as you have told it is not in your book.

 

[snshusat161]

Okay, I did as you said and...
A and B came back with -1
B and C came back with -1

I'm not sure what I am supposed to tell from that ... does "-1" on both mean that they are collinear?

no, it means that both are parallel but do you ever heard parallel lines intersecting at any point, therefore both lines AB and BC are not parallel but the same line and since points A, B and C lies on the same line they are collinear.

And "-1" doesn't mean that they are collinear. Any number will do well if you get it for both AB and BC.

Yes, "-1" on both means they have the same slope, and since they also share a point, they must be on the same line.

(incidentally, of course, if you check A and C, you should find the same )

I've said "No" and then just in very next post Tiny Tim has said "Yes", I think You are very confused. I want to clear it to you as well as Tiny Tim

Tiny Tim has said Yes for the current problem where you are getting a slope of "-1" but I've said No to tell you that every time in such problem you will not get "-1" as your answer. You don't have to care for that number "-1", only thing which you have to care is that whatever you get must be equal for both of the solution you have done.
To make it more clear assume that you have got "5" in place of "-1" but for both the solution then also it is right.