Question
Find the coordinates of point X if it partitions the directed segment overline AB in the ratio 1:2. (1 point) X(-5,-4 2/3 ) X(-1,- 2/3 ) X(-2 1/3 ,-1 1/3 ) X(-5 1/4 ,-2 1/2 )
Answers
Answered by
GPT-4o mini
To find the coordinates of point \( X \) that partitions the directed segment \( \overline{AB} \) in the ratio \( 1:2 \), we need the coordinates of points \( A \) and \( B \).
However, you have not provided the coordinates of points \( A \) and \( B \). Let’s denote the coordinates of point \( A \) as \( (x_1, y_1) \) and the coordinates of point \( B \) as \( (x_2, y_2) \).
The formula for finding a point that divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \) is given by:
\[
X\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)
\]
In your case, the ratio \( m:n \) is \( 1:2 \), so \( m = 1 \) and \( n = 2 \).
Using this ratio, the coordinates of point \( X \) can be derived as follows:
\[
X\left(\frac{1 \cdot x_2 + 2 \cdot x_1}{1 + 2}, \frac{1 \cdot y_2 + 2 \cdot y_1}{1 + 2}\right)
\]
Now substituting the values:
\[
X\left(\frac{x_2 + 2x_1}{3}, \frac{y_2 + 2y_1}{3}\right)
\]
Without knowing specific coordinates for points \( A \) and \( B \), I cannot calculate the exact coordinates for point \( X \).
If you can provide the coordinates of points \( A \) and \( B \), I will be able to calculate the coordinates for point \( X \). Alternatively, if the points \( (-5, -4 \frac{2}{3}), (-1, - \frac{2}{3}), (-2 \frac{1}{3}, -1 \frac{1}{3}), (-5 \frac{1}{4}, -2 \frac{1}{2}) \) are options for potential coordinates of \( X \), then we can use them to see if they match the computed values for the specified ratio. Let me know how you'd like to proceed!
However, you have not provided the coordinates of points \( A \) and \( B \). Let’s denote the coordinates of point \( A \) as \( (x_1, y_1) \) and the coordinates of point \( B \) as \( (x_2, y_2) \).
The formula for finding a point that divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \) is given by:
\[
X\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)
\]
In your case, the ratio \( m:n \) is \( 1:2 \), so \( m = 1 \) and \( n = 2 \).
Using this ratio, the coordinates of point \( X \) can be derived as follows:
\[
X\left(\frac{1 \cdot x_2 + 2 \cdot x_1}{1 + 2}, \frac{1 \cdot y_2 + 2 \cdot y_1}{1 + 2}\right)
\]
Now substituting the values:
\[
X\left(\frac{x_2 + 2x_1}{3}, \frac{y_2 + 2y_1}{3}\right)
\]
Without knowing specific coordinates for points \( A \) and \( B \), I cannot calculate the exact coordinates for point \( X \).
If you can provide the coordinates of points \( A \) and \( B \), I will be able to calculate the coordinates for point \( X \). Alternatively, if the points \( (-5, -4 \frac{2}{3}), (-1, - \frac{2}{3}), (-2 \frac{1}{3}, -1 \frac{1}{3}), (-5 \frac{1}{4}, -2 \frac{1}{2}) \) are options for potential coordinates of \( X \), then we can use them to see if they match the computed values for the specified ratio. Let me know how you'd like to proceed!