line segment AB is bisected at point G by ray XY. Which of the following is true about point G? Draw a picture to help you answer the question.
A. G is the midpoint of ray XY.
B. G is both the midpoint of ray XY and the midpoint of line segment AB.
C. G is the midpoint of line segment AB.
D. None of these
C. G is the midpoint of line segment AB.
Picture:
```
A----(G)----B
|
|
XY
```
The ray XY bisects AB at G, meaning that G is the point that divides AB into two equal halves. Therefore, G is the midpoint of AB. Option B is not necessarily true, as G may not be the midpoint of XY (it depends on the specific location of X and Y). Option A is not true, as G cannot be the midpoint of a ray since a ray extends indefinitely in one direction. Option D is not true, as we have determined that G is the midpoint of AB.
To determine which statement is true about point G, let's first draw a diagram.
- Draw a line segment AB.
- Draw a ray XY starting from a point on AB and extending beyond it.
Now, since the line segment AB is bisected by ray XY at point G, point G should be located somewhere on AB, dividing it into two equal segments.
With this information, we can deduce that:
- Statement A ("G is the midpoint of ray XY") is incorrect because point G is not the midpoint of ray XY. It is located somewhere on AB, not on the ray itself.
- Statement B ("G is both the midpoint of ray XY and the midpoint of line segment AB") is also incorrect because point G is not the midpoint of ray XY.
- Statement C ("G is the midpoint of line segment AB") is the correct answer. Point G is indeed the midpoint of line segment AB since it divides the line segment into two equal halves.
Thus, the correct answer is C.