A(4,-1) b(0,7) c(2,m) this is a triangle center of gravity of the triangle on the x-axis what is the triangle area. emergency emergency emergency

The center of gravity of a triangle is also known as the centroid, the meet of the medians, the segments from the midpoint of a side to the opposite vertex.

The centroid is easily calculated from the average of the coordinates. We know the centroid is on the x axis, i.e. the y coordinate is 0. That's the equation:

Now we have the three vertices of a triangle. We can calculate the area with the shoelace formula:

(4,-1),(0,7),(2,-6)

(0,7),(2,-6),(4,-1)

18

The given information is

When she adds 2 to both sides, the equation

Subtracting 3x to both sides

So the equation has exactly one solution which is