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

Question

Please help in this subject, Partitioning Directed Segments on the Coordinate Plane

Answer 1

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

The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2

d= 4 (13)^(1/2)

Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)

Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).

Hence the mid point of AQ is P which can found out again using the mid point formula

P= [(-1+3)/2,(2+8)/2]= (1,5)

Final answer: P=(1,5)