Find a Point that Partitions a
Segment in a Given Ratio a:b
a
 a

 a  b  x2  x1   x1, a  b  y 2  y1   y1 


Find the coordinates of P along the directed line
segment AB so that the ratio of AP to PB is 3 to 2.
In order to divide
the segment in the
ratio of 3 to 2, think
of dividing the
segment into 3 + 2
or 5 congruent
pieces.
A(3, 4), B(6, 10); 3 to 2.
3
6
AB has a rise of 6.
AB has a run of 3.
A(3, 4), B(6, 10); 3 to 2.
To find the coordinates
of point P…
a
 a

 a  b  run  x1, a  b  rise   y1 


3
3

 5  3   3, 5 6   4 


 4.8, 7.6 
3
6
Example 1: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.
a
 a

x

x

x
,
y

y

y
 2 1 1 
1
1
a b 2
ab


4
4

 5  7   1, 5 1  3 


6.6, 3.8 
Example 2: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.
a
 a

x

x

x
,
y

y

y
 2 1 1 
1
1
a b 2
ab


3
 3

 10  6   2, 10  4   1


 0.2, 2.2 
Example 3: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.
a
 a

x

x

x
,
y

y

y
 2 1 1 
1
1
a b 2
ab


1
1

 5  5   8, 5  2   0 


7,
 0.4 
Example 4: Find the coordinates of point P
along the directed line segment AB so that AP to
PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.
a
 a

x

x

x
,
y

y

y
 2 1 1 
1
1
a b 2
ab


3
3

 5  8   2, 5  5   4 


 2.8,
 1