Answer:
7:10
Step-by-step explanation:
1) to determine the equation of the line with the given points (-2;3) and (4;5):
[tex]\frac{x+2}{4+2} =\frac{y-3}{5-3}; \ => \ \frac{x+2}{3} =\frac{y-3}{1}; \ <=> \ x-3y=-11.[/tex]
2) to calculate the coordinates of intersection point:
[tex]\left \{ {{4x+5y=21} \atop {x-3y=-11}} \right. \ <=> \ \left \{ {{y=\frac{65}{17}} \atop {x=\frac{8}{17}}} \right.[/tex]
3) to calculate the required ratio:
[tex]\frac{d_1}{d_2}=\frac{\sqrt{(-2-\frac{8}{17} )^2+(3-\frac{65}{17} )^2}}{\sqrt{(4-\frac{8}{17} )^2+(5-\frac{65}{17} )^2}}=\frac{7}{10}.[/tex]
