Answer:
Step-by-step explanation:
Here's the basic rule for this:
If P with coordinates [tex](x_{p},y_{p})[/tex] divides a line segment from A with coordinates [tex](x_{1},y_{1})[/tex] to B with coordinates [tex](x_{2},y_{2})[/tex] in the ratio a:b, then
[tex]x_{p}=x_{1}+\frac{a}{a+b}(x_{2}-x_{1})[/tex] and
[tex]y_{p}=y_{1}+\frac{a}{a+b}(y_{2}-y_{1})[/tex]
Our [tex]x_{p}[/tex] fills in as follows:
[tex]x_{p}=1+\frac{4}{4+1}(8-1)[/tex] which simplifies to
[tex]x_{p}=1+\frac{4}{5}(7)[/tex] which further simplifies to
[tex]x_{p}=1+\frac{28}{5}[/tex] and
[tex]x_{p}=\frac{5}{5}+\frac{28}{5}[/tex] which gives us, finally, that
[tex]x_{p}=\frac{33}{5}=6.6[/tex]
Our [tex]y_{p}[/tex] fills in as follows:
[tex]y_{p}=3+\frac{4}{4+1}(4-3)[/tex] which simplifies to
[tex]y_{p}=3+\frac{4}{5}(1)[/tex] which simplifies to
[tex]y_{p}=\frac{15}{5}+\frac{4}{5}[/tex] which gives us, finally, that
[tex]y_{p}=\frac{19}{5}=3.8[/tex]
Choice C is the one you want!
