To find the coordinates of the fourth vertex, D, in the parallelogram with vertices S(-1, -1), A(1,4), and M(2,-1), we can use the midpoint formula. The midpoint of segment SA is (0, 1.5), and the midpoint of segment SM is (0.5, -1). Since the line connecting the midpoints of SA and SM is parallel to AD, the midpoint of AD is also (0.5, -1). By adding the x-coordinate of S to the x-coordinate of the midpoint of AD and the y-coordinate of S to the y-coordinate of the midpoint of AD, we find that D is located at (-0.5, -2).
The coordinates of the fourth vertex, D, can be found by using the properties of a parallelogram. In a parallelogram, opposite sides are equal in length and parallel to each other. To find the coordinates of D, we can use the midpoint formula.
First, let's find the midpoint of segment SA. The x-coordinate of the midpoint is the average of the x-coordinates of S and A, and the y-coordinate is the average of the y-coordinates. So, the midpoint of SA is ((-1 + 1)/2, (-1 + 4)/2) = (0, 1.5).
Now, let's find the midpoint of segment SM. Using the same formula, the midpoint of SM is ((-1 + 2)/2, (-1 + (-1))/2) = (0.5, -1).
Since opposite sides of a parallelogram are parallel, we know that the line connecting the midpoints of SA and SM is parallel to AD. Therefore, the midpoint of AD is the same as the midpoint of SM, which is (0.5, -1).
To find the coordinates of D, we can use the fact that the x-coordinate of D is the sum of the x-coordinate of S and the x-coordinate of the midpoint of AD, and the y-coordinate of D is the sum of the y-coordinate of S and the y-coordinate of the midpoint of AD. So, D is ((-1 + 0.5), (-1 + (-1))) = (-0.5, -2).
Therefore, the coordinates of the fourth vertex, D, are (-0.5, -2).
The question probable may be:
S(-1, -1), A(1,4), M(2,-1) are three of the four vertices of a parallelogram. Find the coordinates of the fourth vertex D.