Mathematics

Problem

Points

A(3,7)

and

B(9,1)

are fixed. Which statement is always true for any point

P

that divides

AB

internally in the ratio

m:n

, where

m,n>0

? a) Exactly one of the coordinates of

P

lies strictly between the corresponding coordinates of

A

and

B

. b) Both the

x

- and

y

-coordinates of

P

lie strictly between the respective coordinates of

A

and

B

. c) Both coordinates of

P

are always greater than those of

A

. d) The

x

-coordinate of

P

is always less than its

y

-coordinate.