Answer:
(19, 10)
Step-by-step explanation:
To find the coordinates of a point that partitions segment AB in the ratio 1 : 5, we can use the internal section formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Internal Section Formula}} \\\\P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\\\\\textsf{where:}\\\phantom{ww}\bullet \;\textsf{$(x_1,y_1)$ are the coordinates of the first endpoint.}\\\phantom{ww}\bullet \;\textsf{$(x_1,y_1)$ are the coordinates of the second endpoint.}\\\phantom{ww}\bullet\;\textsf{$m$ and $n$ are the ratio values in which $P$ divides the line internally.}\end{array}}[/tex]
In this case:
Substitute the values into the formula:
[tex]P(x,y)=\left(\dfrac{1\cdot 34+5\cdot 16}{1+5},\dfrac{1\cdot 40+5\cdot 4}{1+5}\right)[/tex]
Simplify:
[tex]P(x,y)=\left(\dfrac{34+80}{6},\dfrac{40+20}{6}\right)\\\\\\\\P(x,y)=\left(\dfrac{114}{6},\dfrac{60}{6}\right)\\\\\\\\P(x,y)=\left(19,10\right)[/tex]
Therefore, the coordinates of the point that partitions segment AB in the ratio 1 : 5 are:
[tex]\Large\boxed{\boxed{\left(19,10\right)}}[/tex]
