Final answer:
To determine the coordinates of point A with midpoint M at (-1,2) and point B at (3,-5), the midpoint formula in reverse was used. The calculated coordinates for point A are (-5, 9), which is not listed in the provided options. The closest given option is (-5,10), though it is not correct.
Step-by-step explanation:
To find the location of point A given the midpoint M at (-1,2) and point B at (3,-5), we can use the midpoint formula in reverse. The midpoint is calculated as M = ((x1 + x2) / 2, (y1 + y2) / 2), where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Since we know the coordinates of M and B, we can set up a system of equations to solve for the coordinates of point A.
Let's denote the coordinates of A as (x, y). So we have the following equations:
- (x + 3) / 2 = -1
- (y - 5) / 2 = 2
By solving these equations, we get:
- x + 3 = -2 ⇒ x = -5
- y - 5 = 4 ⇒ y = 9
Therefore, the coordinates of point A are (-5, 9). However, this option is not listed in the provided choices, indicating a potential error either in the question or in the provided options. Based on the choices given, option 2: (-5,10) is the closest to our computed answer, but it's still different by 1 in the y-coordinate.