Question

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

Answer 1

7:10

Explanation:

1) to determine the equation of the line with the given points (-2;3) and (4;5):

`(x+2)/(4+2) =(y-3)/(5-3); \ => \ (x+2)/(3) =(y-3)/(1); \ <=> \ x-3y=-11.`

2) to calculate the coordinates of intersection point:

`\left \{ {{4x+5y=21} \atop {x-3y=-11}} \right. \ <=> \ \left \{ {{y=(65)/(17)} \atop {x=(8)/(17)}} \right.`

3) to calculate the required ratio:

`(d_1)/(d_2)=\frac{\sqrt{(-2-(8)/(17) )^2+(3-(65)/(17) )^2}}{\sqrt{(4-(8)/(17) )^2+(5-(65)/(17) )^2}}=(7)/(10).`