Point P divides AB with A(-4,-5) and B(2,4) in a ratio of 1:5.
Therefore, the ratio of 1:5 is also m1= 1 and m2= 5. Then, we must use the following formula:
[tex]\begin{gathered} P=\text{ \lparen}\frac{m1x2+m2x1}{m1\text{ + m2}},\frac{m1y2+m2y1}{m1\text{ + m2}}) \\ \\ P=\text{ \lparen}\frac{\lparen1\lparen2\rparen+5\lparen-4\rparen\rparen}{1\text{ + 5}},\text{ }\frac{\lparen1\lparen4\rparen+5\lparen\text{ -}5\rparen\rparen}{1+\text{ 5}}) \\ \\ P=\text{ \lparen}\frac{\lparen2-20\rparen}{6},\text{ }\frac{\lparen4\text{ -}25\rparen}{6}) \\ \\ P=\text{ \lparen}\frac{-18}{6},\text{ }\frac{\text{ -21}}{6}) \\ \\ P=\text{ \lparen-3, -3.5 }) \end{gathered}[/tex]
Then, P is located at (-3, -3.5. Answer D.
