# problem of proving the points lie on the straight line

• September 2nd 2010, 02:08 PM
ziaharipur
problem of proving the points lie on the straight line
I have following question.

Prove that (1,1) , (-2,-8) and (4,10) lie on straight line.

Now its very easy if we use the slop technique that is we find slop of first two points (1,1) and (-2,-8) which is 3 similarly we find slop of the points (-2,-8) and (4,10) which is also 3. as the slops are equal therefore the points lie on the straight line.

But the problem is here we need to prove it by Distance formula. how can we do this?
• September 2nd 2010, 02:26 PM
skeeter
Quote:

Originally Posted by ziaharipur
I have following question.

Prove that (1,1) , (-2,-8) and (4,10) lie on straight line.

Now its very easy if we use the slop technique that is we find slop of first two points (1,1) and (-2,-8) which is 3 similarly we find slop of the points (-2,-8) and (4,10) which is also 3. as the slops are equal therefore the points lie on the straight line.

But the problem is here we need to prove it by Distance formula. how can we do this?

show AB + BC = AC
• September 2nd 2010, 02:27 PM
wonderboy1953
A comment. Two straight lines can have the same slope doesn't mean that all three points are on the same line.
• September 2nd 2010, 02:31 PM
Quote:

Originally Posted by ziaharipur
I have following question.

Prove that (1,1) , (-2,-8) and (4,10) lie on straight line.

Now its very easy if we use the slope technique.. that is, we find slope of the line joining the first two points (1,1) and (-2,-8), which is 3... similarly we find slope of the line joining the points (-2,-8) and (4,10) which is also 3. As the slopes are equal, therefore the points lie on a straight line.

But the problem is here we need to prove it by Distance formula. how can we do this?

How you do it with the distance formula (point co-ordinate form of Pythagoras' theorem),
is to calculate the distance from (-2,-8) to (1,1).
Then calculate the distance from (1,1) to (4,10).

Finally calculate the distance between the points that are furthest away... from (-2,-8) to (4,10).

If the longest distance (the 3rd one mentioned above) is the sum of the first 2 distances,
then the points lie on a straight line.
• September 2nd 2010, 02:49 PM
Plato
Do not make it hard.
Show that the point pairs $(1,1)~\&~(-2,-8)$ and $(1,1)~\&~(4,10)$ determine the same slope.
• September 2nd 2010, 03:24 PM
bigwave
same equations
Quote:

Originally Posted by ziaharipur
I have following question.

Prove that (1,1) , (-2,-8) and (4,10) lie on straight line.

Now its very easy if we use the slop technique that is we find slop of first two points (1,1) and (-2,-8) which is 3 similarly we find slop of the points (-2,-8) and (4,10) which is also 3. as the slops are equal therefore the points lie on the straight line.

But the problem is here we need to prove it by Distance formula. how can we do this?

one way anyway is to show the set of any 2 of the 3 points results in the same equation

for $(1,1)$ and $(-2,-8)\ m = 3$
$y-1 = 3(x-1) \Rightarrow y=3x-2$

and for $(-2,-8)$ and $(4,10)\ m=3$
$y+8=3(x+2) \Rightarrow y=3x-2$

the equations are the same so the points are on the same line
the distance formula would be more work..
• September 2nd 2010, 04:34 PM