Question

11 of 1511 of 15 Items Question Use the image to answer the question. Find the coordinates of point X if it partitions the directed segment AB¯¯¯¯¯¯¯¯ in the ratio 1:2. (1 point) Responses (−213, −113) (−213, −113) (−514, −212) (−514, −212) (−1, −23) (−1, −23) Skip to navigation page 1 of 1

Answer 1

To find the coordinates of point X that partitions the directed segment AB in the ratio of 1:2, we can use the section formula. The section formula states that if a point \( P(x, y) \) divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of point \( P \) can be calculated as follows:

\[ P\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

Here, \( A \) and \( B \) are the endpoints of the segment, and \( m:n = 1:2 \).

To apply this formula, we need the coordinates of points \( A \) and \( B \). Since the coordinates of points \( A \) and \( B \) are not provided in your question, please share those coordinates so we can calculate the coordinates of point \( X \).