Mathematics

Problem

For the two fixed points

A(2,4)

and

B(10,8)

on a coordinate plane, consider an internal division point

R

that partitions the line segment

AB

in the ratio

k:1

where

k

is a positive real number measured from

A

B

. a. (i) In terms of

k

, find the coordinates of

R

. b. (ii) Show algebraically that as

k

becomes very large, the coordinates of

R

approach those of

B

. Explain what this indicates about the position of

R

on the segment. c. (iii) When

k=1

, compute the exact coordinates of

R

and state how

R

divides

AB

in this special case.