To find the position vector of point D, which divides the line segment AB in the ratio 1:1, you can follow these steps:
1. Identify the coordinates of points A and B:
- Point A has coordinates (37, 67).
- Point B has coordinates (57, -27).
2. Understanding the ratio:
- Since the ratio is 1:1, point D is the midpoint of the line segment AB.
3. Midpoint formula:
- The midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be found using the formula:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
4. Apply the coordinates of points A and B:
- For x-coordinates:
[tex]\[
\frac{37 + 57}{2} = \frac{94}{2} = 47
\][/tex]
- For y-coordinates:
[tex]\[
\frac{67 + (-27)}{2} = \frac{67 - 27}{2} = \frac{40}{2} = 20
\][/tex]
5. Combining the results:
- The coordinates of point D are (47.0, 20.0).
Therefore, the position vector of the point D is [tex]\((47.0, 20.0)\)[/tex].
