Question

Point R is located at  (3,2) and point S is located at (8,15) . What are the coordinates of the point that partitions the directed line segment RS in a 1:3 ratio

Answer 1

The coordinates of the point can be solve using the fomula:

x = x1 + r( x2 - x1 )
y = y1 + r( y2 - x1)
where r is the ratio that partitions the segment
x = x1 + r( x2 - x1 )
x = 3 + 1/3( 8 - 3 )
x = 3 + 1/3( 5 )
x = 14/3
y = y1 + r( y2 - x1)
y = 2 + 1/3( 15 - 2)
y = 2 + 1/3( 13 )
y = 19/3
so the coordinate is ( 14/3 , 19/3 )