Final answer:
The midpoints of the diagonals of a parallelogram with vertices A(-5, -1), B(1, 1), C(4, 9), and D(-2, 7) are both M1 and M2, located at (-0.5, 4). This is calculated using the midpoint formula for each diagonal of the parallelogram.
Step-by-step explanation:
To find the midpoints of the diagonals of a parallelogram, first identify the endpoints of each diagonal. For the parallelogram with vertices A(-5, -1), B(1, 1), C(4, 9), and D(-2, 7), the diagonals are AC and BD. Use the midpoint formula which is ((x1+x2)/2, (y1+y2)/2) to find the midpoint of each diagonal.
For diagonal AC, the midpoint M1 is calculated as follows:
- M1 = ((-5+4)/2, (-1+9)/2)
- M1 = (-0.5, 4)
For diagonal BD, the midpoint M2 is calculated as:
- M2 = ((1-2)/2, (1+7)/2)
- M2 = (-0.5, 4)
Interestingly, both midpoints for the diagonals AC and BD are the same point, which is (-0.5, 4).