Final answer:
To find the area of the triangle formed by points B, B', and C, we can use the formula for the area of a triangle. The area is given by (base * height) / 2. The base of the triangle is the distance between B and B', and the height is the distance between C and the x-axis.
Step-by-step explanation:
To find the area of the triangle formed by points B, B', and C, we need to know the coordinates of these points. Let's assume that the coordinates of point B are (x, y). When B is reflected over the y-axis, the x-coordinate becomes -x. Therefore, the coordinates of point B' are (-x, y). The coordinates of point C can be calculated by finding the midpoint of B and B', which is ((x+(-x))/2, (y+y)/2) = (0, 2y).
Next, we can use the formula for the area of a triangle, which is (base * height) / 2. The base of the triangle can be calculated by finding the distance between B and B', which is 2x, and the height can be calculated by finding the distance between C and the x-axis, which is the y-coordinate of C, which is 2y. Therefore, the area of the triangle is (2x * 2y) / 2 = 2xy.
In summary, the area of the triangle formed by points B, B', and C is 2xy.