If A = (-4, 6) and B = (6, -7) find:
I) the coordinates of P, where P € AB and AP:PB = 3:1
ii) the coordinates of P, where P € AB and AP:AB = 3:1
Hello scubasteve94I'm sure you know the formula for finding the coordinates of the mid-point of the line joining to . It is:Well, there's a more general formula for the coordinates of the point that divides in the ratio . It is this:
(If you understand vector notation, this is equivalent to , where are the position vectors of and .)
For part (i), , so . So plug these values into the formula, using .
For part (ii), we have . So lies outside the line segment . Draw a diagram if you're not sure. You'll then find that the ratio . So you'll need to use the values .
Here are my answers:Spoiler:
Can you complete it now?
Grandad