To determine the location of point \( L \) that divides the segment \( \overline{AB} \) in the ratio 1:3, we need to know the coordinates of points \( A \) and \( B \).
Let’s denote:
- The coordinates of point \( A \) as \( (x_1, y_1) \)
- The coordinates of point \( B \) as \( (x_2, y_2) \)
The formula for finding a point \( L \) that divides the segment \( \overline{AB} \) in the ratio \( m:n \) is:
\[ L = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
In this case, since \( L \) divides \( AB \) in the ratio \( 1:3 \), we have \( m = 1 \) and \( n = 3 \).
Substituting these values into the formula gives us:
\[ L = \left( \frac{1 \cdot x_2 + 3 \cdot x_1}{1 + 3}, \frac{1 \cdot y_2 + 3 \cdot y_1}{1 + 3} \right) = \left( \frac{x_2 + 3x_1}{4}, \frac{y_2 + 3y_1}{4} \right) \]
To find the specific coordinates of point \( L \), we need the coordinates of points \( A \) and \( B \). Since the question refers to points on a coordinate plane and gives options for the coordinates of point \( L \), you will need to calculate based on the known coordinates of \( A \) and \( B \).
Please provide the coordinates of points \( A \) and \( B \) so that we can accurately compute the coordinates of point \( L \).
1 answer