Questions: (-6,-2) ratio 1:4 S(5,6)

Solution Steps

To find the point that divides the line segment joining the points \((-6, -2)\) and \(S(5, 6)\) in the ratio 1:4, we can use the section formula. The section formula for a point dividing a line segment in the ratio \(m:n\) is given by: \[ \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

1. Identify the coordinates of the points and the ratio.
2. Apply the section formula to find the coordinates of the dividing point.

Given points are \((-6, -2)\) and \( (5, 6) \). The ratio is \(1:4\).

The section formula for a point dividing a line segment in the ratio \(m:n\) is: \[ \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \] Substituting the given values: \[ x = \frac{1 \cdot 5 + 4 \cdot (-6)}{1 + 4} = \frac{5 - 24}{5} = \frac{-19}{5} = -3.8 \] \[ y = \frac{1 \cdot 6 + 4 \cdot (-2)}{1 + 4} = \frac{6 - 8}{5} = \frac{-2}{5} = -0.4 \]

Final Answer