Answer:
The coordinates of M are M(2, 1).
Step-by-step explanation:
Let the coordinates of M be M(x, y) that divides the line segment joining the points A(-1, -3) and B(8, 9) in the ratio of 1 : 2.
By section formula, we know that coordinates of a point (x, y) that divides the line segment joining the points (x₁, y₁) and (x₂, y₂) in the ratio of m₁ : m₂ are given by,
[tex]x=\frac{m_{1}x_{2} +m_{2}x_{1}}{m_{1}+m_{2}}[/tex]
[tex]y=\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}[/tex]
Now, (x₁, y₁) = (-1, -3); (x₂, y₂) = (8, 9); m₁ : m₂ = 1 : 2.
Now, we will substitute the values of (x₁, y₁), (x₂, y₂) and m₁ : m₂ in the above mentioned section formula.
The coordinates of M(x, y ) are given by,
[tex]x = \frac{1\times 8+2\times(-1) }{1+2} =\frac{8-2}{3} =2\\y = \frac{1\times9+2\times(-3)}{1+2} =\frac{9-6}{3} = 1[/tex]
So, the coordinates of M are M(2, 1).
