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In what ratio does the line of the equation 4x + 5y = 21 divide the line segment joining the points (-2,3) and (4,5)​

Sagot :

evgeniylevi

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]

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