Final answer:
By using the midpoint formula, we can deduce that the coordinates of point B are (-22, 10), as it is the endpoint opposite to A of the segment AB with a given midpoint.
Step-by-step explanation:
To find the location of point B, we utilize the concept of the midpoint in coordinate geometry. The midpoint formula states that the midpoint M(x,y) of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). Since we know that M is at (-10, 3) and A is at (2, -4), we can set up the following equations to solve for B's coordinates:
M_x = (A_x + B_x)/2 \\ M_y = (A_y + B_y)/2
Substituting the given values leads to:
(-10) = (2 + B_x)/2
3 = (-4 + B_y)/2
By solving these equations, we find that:
- B_x = -10 * 2 - 2 = -22
- B_y = 3 * 2 + 4 = 10
Therefore, the coordinates of point B are (-22, 10).