The given points are:
A = (8, 0)
B = (3, 22)
We need to find the point P that divides the segment AB so that AP to PB is 1:4
Let's say
(x1, y1) = (8, 0)
(x2, y2) = (3, 22)
First ratio = m1 = 1
Second ratio = m2 = 4
To find the missing coordinates of P (x,y), we will use the section formula, that is:
[tex](x,y)\text{ = (}\frac{m1x2+\text{ m2x1}}{m2+m1},\frac{m1y2\text{ + m2y1}}{m2+m1}\text{)}[/tex]
Now, by solving it
[tex](x,y)\text{ = (}\frac{1\cdot3+\text{ 4}\cdot8}{4+1},\frac{1\cdot22\text{ + 4}\cdot0}{4+1}\text{)}[/tex][tex](x,y)\text{ = (}\frac{3+32}{5},\frac{22\text{ + }0}{5}\text{)}[/tex][tex](x,y)\text{ = (}\frac{35}{5},\frac{22\text{ }}{5}\text{)}[/tex][tex](x,y)\text{ = (7},4.4\text{)}[/tex]
Hence, the coordinates of point P are (7, 4.4).
