To find the coordinates of point C that divides the line segment from point A(0, 0) to point B(-8, 2) in the ratio 1:4, we can use the section formula.
If point C divides the segment AB in the ratio \( m:n \), the coordinates of point C can be determined using the formula:
\[ C_x = \frac{n \cdot A_x + m \cdot B_x}{m+n} \]
\[ C_y = \frac{n \cdot A_y + m \cdot B_y}{m+n} \]
In your case, \( A(0, 0) \) and \( B(-8, 2) \), with the ratio 1:4 (where \( m = 1 \) and \( n = 4 \)).
Substituting into the formulas:
- Calculate \( C_x \):
\[ C_x = \frac{4 \cdot 0 + 1 \cdot (-8)}{1 + 4} = \frac{0 - 8}{5} = \frac{-8}{5} = -1.6 \]
- Calculate \( C_y \):
\[ C_y = \frac{4 \cdot 0 + 1 \cdot 2}{1 + 4} = \frac{0 + 2}{5} = \frac{2}{5} = 0.4 \]
Thus, the coordinates of point C are:
\[ C(-1.6, 0.4) \]