Final answer:
To find the other endpoint of the segment, given the midpoint (-3,4) and one endpoint (-7,6), use the midpoint formula in reverse to solve for the other endpoint's coordinates, resulting in the other endpoint being at (1,2).
Step-by-step explanation:
The question involves finding the other endpoint of a line segment when given the midpoint and one endpoint. This falls under the category of coordinate geometry, specifically the midpoint formula. To find the other endpoint, one can apply the midpoint formula in reverse. Given the midpoint M(-3,4) and one endpoint A(-7,6), we can label the other endpoint as B(x,y). Using the midpoint formula, M = ((x1 + x2)/2, (y1 + y2)/2), we can solve for the coordinates of B. Applying the midpoint formula, we have:
- -3 = (-7 + x)/2
- 4 = (6 + y)/2
To find x, we multiply both sides of the first equation by 2 and add 7:
- -3 × 2 = -7 + x
- -6 + 7 = x
- x = 1
To find y, we multiply both sides of the second equation by 2 and subtract 6:
- 4 × 2 = 6 + y
- 8 - 6 = y
- y = 2
Thus, the other endpoint B of the segment is at (1,2).