p is in AB, The ratio of AP to PB is 3 to 1.... (right?)
I.
AB:
AP:
PB:
and just use and
to figure out the coordinates.
If this is correct just do the same for II,
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