Final answer:
To find the other endpoint when given one endpoint and the midpoint of a line segment, you can rearrange the midpoint formula. The calculations show that the other endpoint B is at (-15, 7).
Step-by-step explanation:
To find the other endpoint of a line segment when you are given one endpoint and the midpoint, you can use the midpoint formula. The midpoint formula is found by taking the averages of the x-coordinates and the y-coordinates of the endpoints respectively:
Midpoint M (x_m, y_m) = ((x_1 + x_2)/2, (y_1 + y_2)/2)
Given that we know the midpoint M (-4, 3) and one endpoint A (7, -1), we can find the coordinates of the other endpoint B (x_2, y_2) by using the formula. We rearrange the formula to solve for x_2 and y_2:
x_2 = 2x_m - x_1
y_2 = 2y_m - y_1
So the calculations will look like this:
- x_2 = 2(-4) - 7
- x_2 = -8 - 7
- x_2 = -15
- y_2 = 2(3) - (-1)
- y_2 = 6 + 1
- y_2 = 7
Therefore, the coordinates of the other endpoint B are (-15, 7).