Equation for dividing a point AB internally/externaly (1 Viewer)

[Managore]

Quick.. what's the equations for a point that divides AB internally or externally in the ratio p:q

 

[smallcattle]

(px2 + qx1) /(p+q) , (py2 + qy1) / (p+q)

just change to -p:q when dividing externally

 

[tempco]

[px₂ + qx₁]/[p + q]

Same as y.

If it's internally, keep p and q the same.

If it's externally, negative the smaller value... eg. 3:2 externally, make it 3:-2.

EDIT: Bah.

 

[Managore]

thankyou thankyou

 

[smallcattle]

[px₂ + qx₁]/[p + q]

Same as y.

If it's internally, keep p and q the same.

If it's externally, negative the smaller value... eg. 3:2 externally, make it 3:-2.

EDIT: Bah.

not necessarily

 

[tempco]

Um, that's how I've learnt it... care to give an example where it's not true?

 

[Managore]

wait - as a hypethetical, say if you had the following:

a point C that divides externally a and b in the ratio 1:2

What would, graphically, be correct:

C- - - - - - -A- - - - - - - - - - - - - - -B

C- - - - - - - - - - - - - - -A- - - - - - -B

A- - - - - - -B- - - - - - - - - - - - - - -C

A- - - - - - - - -- - -- - - B- - - - - -- C

A- - - - - - - - - - -B- - - - - - - - - - -C

C- - - - - - - - - - -A- - - - - - - - - - -B

 

[tempco]

C - - - A - - - B
'_____'
'__________'


ACs 1 unit, and BCs 2 units.

I think.

 

[Managore]

so if the ratio is 1:2 external its always on the A side? This has always confused me.. and now at nearly 11pm the night before I'm about to find out

 

[mojako]

Um, that's how I've learnt it... care to give an example where it's not true?

try with any values / questions.

it doesn't matter which one you make negative.

 

[mojako]

so if the ratio is 1:2 external its always on the A side? This has always confused me.. and now at nearly 11pm the night before I'm about to find out

P divides AB in 3:2 externally means:
AP is the 3, PB is the 2 (the shorter one)
(also this means B is between A and P)

P divides BA in 3:2 means:
BP is the 3.

 

[tempco]

Yer I think so... and if the ratio was 2:1, it would be:

A - - - B - - - C

and having the lesser ratio being negative makes sense... AC in the + direction ( --> ) and CB in the - direction ( <-- ). So in the equation it'd be 2:-1.

As for 1:2, AC is in the - direction ( <-- ) and CB is in the + direction ( --> ), so it would be -1:2.

*shrugs* I have no idea what I'm talking about.

EDIT: Hrm... it doesn't make a difference. o____O

 

[CrashOveride]

dudes just use the formula, nothing to it

 

[mojako]

it doesnt matter which +ve direction you choose

btw to those who are not desperately needing to study, I suggest you go to sleep soon.
maths needs concentration.
also dont wake up early tomorrow.

 

[CrashOveride]

dont listen to mojo guys
ill be on here 5am, if u need help just post ill help

 

[Rorix]

doing ratio questions by inspection is cooooool


but ill have to resort to algebra to get both marks, probably

 

[smallcattle]

why are you doing everything by inspection..

 

[Rorix]

its what all the cool kids do

 

[Managore]

Ah I finally get it.. I like doing it by inspection, makes more sense to me than a formula, but I'll state the formula as well, in case I get inspection wrong. Thanks everyone

 

[Kirsti]

ill be on here 5am...

pfft! liar