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Sagot :
The points we have are:
[tex]\begin{gathered} M\mleft(5,-2\mright) \\ N\mleft(-7,6\mright) \end{gathered}[/tex]We label this points as follows for reference:
[tex]\begin{gathered} x_1=5 \\ y_1=-2 \\ x_2=-7 \\ y_2=6 \end{gathered}[/tex]We have that the ratio is:
[tex]1\colon3[/tex]Where we will call a=1 and b=3.
And we use the following formula for finding the coordinates of a point given the two endpoints and the ratio:
[tex](\frac{bx_1+a_{}x_2}{a+b},\frac{by_1+ay_2}{a+b})[/tex]Substituting our values:
[tex](\frac{3(5)+1(-7)}{1+3},\frac{3(-2)+1(6)}{1+3})[/tex]We solve the operations:
[tex](\frac{15-7}{4},\frac{-6+6}{4})[/tex][tex]\begin{gathered} (\frac{8}{4},\frac{0}{4}) \\ (2,0) \end{gathered}[/tex]Point P is at (2,0)
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