What are the coordinates of the point on the directed line segment from (4,−1) to (10,8) that partitions the segment into a ratio of 2 to 1?

Question

I need to find the answer but I'm confused

I need the answer asap plsss!!!

Answer 1

Partitions the line segment in the

ratio A to B...

the x-coordinate is : x1 + A(x2-x1)/(A+B)

the y-coordinate is: y1 + A(y2-y1)/(A+B)

A=2 B=1

X = 4 + 2(10-4)/(2+1)

= 4 + 2*6/3

= 4 + 4

= 8

Y = -1 + 2(8 - -1)/(2+1)

= -1+ 2(9)/3

= -1 + 6

= 5

(8,5) is the point that splits

the line segment into the ratio 2 to 1

check:

distance from (4,-1) to (10,8) is

sqrt( 6^2 + 9^2) = sqrt(36+81) =

sqrt(117) = 3 * sqrt(13)

distancve from (4,-1) to (8,5) is

sqrt( 4^2 + 6^2)

sqrt( 16 + 36) = sqrt(52)

= 2*sqrt(13)

Again the ratio is 2*sqrt(13)/[3*sqrt(13)]

= 2/3

so yes it checks