Question

How can you determine algebraically that the points A(1,2), B(2,4), C(3,6) are on the same line?

Answer 1

define line?

Answer 2

Graph x and y axis

Answer 3

if they have the same difference between them; they are on the same slope

Answer 4

( 1, 2)
+1 +2
------
( 2 , 4)
+1 +2
------
( 3 , 6)

Answer 5

if :

\[\frac{y_1-y_2}{x_1-x_2}=\frac{y_2-y_3}{x_2-x_3}\] then they are on the same line

Answer 6

you can also visualize. from
(1,2) to (2,4) is over one unit, up two. (slope is 2)
then from (2,4) to (3,6) is also over one up two. so yes, on the same line

Answer 7

algebra aint visual lol

Answer 8

it is when you are drawing lines yes?

Answer 9

lines are analytic geometry; now do we 'prove' it algebraically?

Answer 10

yes

Answer 11

when m=m and they share a common point; its proofed

Answer 12

You two stop fighting!! and @amistre: Having the same slope does not necessarily means that they are on the same line. Right?!

Answer 13

yes of course you are right (master) but some thinks are obviously so. i know for a fact that if you had two points (1,2) and (2,4) you would find the slope with your eyeballs, not by subtracting and dividing

Answer 14

mean*

Answer 15

it means they are on the same line f they share a common point right?

Answer 16

Yes, that's right.

Answer 17

yes of course. over 1 up 2, over 1 up 2, over 1 up 2 ...

Answer 18

wish i knew what an inverse transform was. guess i should look it up

Answer 19

In this example, it's so clear that \(y=2x\). So, yes they are on the same line. But if we have much more complicated points, we need to find an equation for the line using two points and then see if the third point lie on the same line by substituting in the equation.

Answer 20

'How can you determine algebraically that .....' ; draw a picture lol

Answer 21

@satellite: What inverse transforms are you talking about?