The point C has position vector (2 3) and point D has position vector (1 2).Find the position vector of the point which divides CD in the ratio 4:-3
I recognized that the minus sign in 4:-3 indicates that it divides the line externally.However,i'm not able to get the ratios right when solving the problem.Can anyone show me with a diagram,the way the ratio is distributed in the line? (< i guess this is where i get it wrong?the ratio part)
Thanks
Hello kandyflossYou're right in saying that the point divides the line segment externally. If , then the ratio of the distances and is , but they are in opposite directions (hence the minus sign). So, from we shall go out 'lengths' to get to and then come back 'lengths' to .
Take a look at the diagram I've attached. You'll see that:Now you probably know that the position vector of the point dividing the line joining the points with position vectors and in the ratio is:
So the point that divides in the ratio has position vector:I hope that clears things up.
Grandad