Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

Question

Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

Answer 1

From A to B, x increases by 8 and y increases by 12

Let P = (x,y)

We are dividing the line segment AB into 4 equal parts (1+3 = 4) with P being 1/4 of the way from A to B along line segment AB.

x = x-coordinate of A plus 1/4 of the change in x from A to B = -1 + (1/4)(8) = 1

y = y-coordinate of A plus 1/4 of the change in y from A to B = 2 + (1/4)(12) = 5

So, P = (1, 5)

Answer 2

If A(a,b) and B(c,d) are the co-ordinates of a line segment, then

[a(1-p)+pb,c(1-p)+dp] are the co-ordinates of the point which divides the segment into pieces in ratio p:(1-p), where 0<p<1.

You should use this information to solve your problem where p=.2.