Stuck on Internal/External Division.

conorkvngh

Was wondering if someone could help me here. The following is the question.
This question comes from Text and Tests 4 LC HL math book

10. A(4,-3) and B (-2,0) are the end points of a line segment. The point P(2-2) divides [AB] internally in the ratio h:k Find the ratio h:k

So I cant get this, its the first time we have been given a question requiring internal/external division without a ratio. The only hint our teacher gave us is that it comes out to a simulatenous equation near the end. I know you can use the line distance formula, and then get its ratio 1:2 but I would rather it in the internal division formula as that is what our teacher would expect. Tried googling etc and found a post from 2012 on this exact question, but no one solved it in internal/external division form. My attempt got me to two equations that are simply wrong and I dont understand where I went wrong.

If you can help thanks!!

ZorbaTehZ

You didnt say what the formula is, google points to this in which i would suggest putting in the values you know Xa, Ya, Xp, ... etc. then you will end up with simultaneous equations precisely as your teacher said.

platypus

conorkvngh wrote: »

Was wondering if someone could help me here. The following is the question.
This question comes from Text and Tests 4 LC HL math book

10. A(4,-3) and B (-2,0) are the end points of a line segment. The point P(2-2) divides [AB] internally in the ratio h:k Find the ratio h:k

So I cant get this, its the first time we have been given a question requiring internal/external division without a ratio. The only hint our teacher gave us is that it comes out to a simulatenous equation near the end. I know you can use the line distance formula, and then get its ratio 1:2 but I would rather it in the internal division formula as that is what our teacher would expect. Tried googling etc and found a post from 2012 on this exact question, but no one solved it in internal/external division form. My attempt got me to two equations that are simply wrong and I dont understand where I went wrong.

If you can help thanks!!

Not really sure why you would go near any equations for this question,seems an overcomplicated approach. Id probably use translations, ie movement from A to P is -2,1 find the movement from P to B and compare to get your ratio

You can also just use distance formula to get length AP and BP then work out the ratio

In general I find using translations for internal/external division of a Line segment an easier and more intuitive method than the formulae, especially for less straightforward questions, so I don't usually use those formulae at all. Obv nothing wrong with using them, up to you really

dlouth15

A trick is to recognise that if you are dealing with a straight line, you only need to consider one of the coordinates, e.g. the x-coordinate of the points. So you could consider that A=4, B=-2 and these two points are divided by P=2. Draw that out on x-axis. How does the point P=2 divide the line segment running from -2 to 4.

Alternatively, taking the y-coordinates of the points, you have a line segment running from -3 to 0 divided by a point at -2.

You should get the same result whether you take the x or y-coordinates and you should be able to do it visually.