what are the coordinates of the point ?

Question

.....that would divide the segment with endpoints from A(-4,1) to B(8,-5) into two segments with a ratio of 1:2 ?

Answer 1

The distance between A and B is 6*√5

The equation of the line through A and B is y = -x/2 - 1

We have a ratio of 1:2. Let d be the length of the shorter segment and 2d the length of the longer segment.

The total length is d+2d=3d so 3d= 6*√5 or d=2*√5.

Let M(x,y) be the point we are looking for. Then distance(AM) = 2*√5

But distance(AM)=√(x-(-4))² + (y-1)²) = √(x-(-4))² + (-x/2-1-1)²) by the distance formula and substituting y=-x/2-1

solve √(x-(-4))² + (-x/2-1-1)²) = 2*√5