Explanation:
If point M is the midpoint of line segment AB, then we know that the coordinates of M are the average of the coordinates of A and B. Therefore, we can set up two equations based on this information, one for the x-coordinate and one for the y-coordinate:
(xA + xB)/2 = -5
(yA + yB)/2 = 4
We can rearrange these equations to solve for one of the variables, say xA or yA, in terms of the other variables:
xA + xB = -10
yA + yB = 8
From these equations, we can see that there are many possible pairs of coordinates for A and B that satisfy the condition that M is the midpoint of AB. For example, if we choose xA = 0, then we can solve for xB and yA in terms of yB:
xB = -10
yA = 8 - yB
So any point A with coordinates (0, 8 - yB) and any point B with coordinates (-10, yB) would have M as the midpoint of AB.
Another example of possible coordinates for A and B could be A(-7, 1) and B(-3, 7), since the midpoint of this line segment is M(-5, 4).
Therefore, there are infinitely many possible pairs of coordinates for point A and B that would have M(-5,4) as the midpoint of line segment AB.