To find the coordinates of point L that divides the segment AB in the ratio 1:3, we can use the section formula.
Let A = (0, 0) and B = (-2, 3). The ratio \( m:n = 1:3 \).
The formula for finding the coordinates of point L that divides the segment AB in the ratio m:n is given by:
\[ L\left(x, y\right) = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
Here:
- \( (x_1, y_1) \) are the coordinates of point A (0, 0)
- \( (x_2, y_2) \) are the coordinates of point B (-2, 3)
- \( m = 1 \) and \( n = 3 \)
Now, substituting the values into the formula, we have:
\[ L\left(x, y\right) = \left( \frac{1 \cdot -2 + 3 \cdot 0}{1 + 3}, \frac{1 \cdot 3 + 3 \cdot 0}{1 + 3} \right) \]
Calculating the x-coordinate:
\[ x = \frac{-2 + 0}{4} = \frac{-2}{4} = -\frac{1}{2} \]
Calculating the y-coordinate:
\[ y = \frac{3 + 0}{4} = \frac{3}{4} \]
Thus, the coordinates of point L are:
\[ L\left(-\frac{1}{2}, \frac{3}{4}\right) \]
Now let's check the options provided in the question. None of them correspond to \( \left(-\frac{1}{2}, \frac{3}{4}\right) \). So there may have been a misunderstanding in the ratio definition from your question or a misalignment with the provided options.
However, if the ratio is indeed \( 1:3 \) and points A and B are as stated, \( L\) is located at these coordinates. To ensure a correct result, you may want to recheck the options provided.
If you have further details or options to verify against, please provide them!
1 answer