Final answer:
To find the measure of point G, we set up an equation using the fact that the distances from G to each of the vertices of the triangle are equal. Solving for x, we find that x = 6. Substituting this value into the expression for G, we find that the measure of point G is -6.
Step-by-step explanation:
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the measure of point G, we need to find the value of x in the expressions for points A, B, and C. Then we can substitute the value of x into the expression for point G.
Given:
- B: 7x - 41
- A: 5x - 19
- C: 28
Since G is the circumcenter, the distances GA, GB, and GC are equal. So we can set up the following equation:
GA = GB
5x - 19 = 7x - 41
Solving for x, we get:
12 = 2x
x = 6
Substituting x = 6 into the expression for G, we get:
G: 9x - 60 = 9(6) - 60 = 54 - 60 = -6
Therefore, the measure of point G is -6.