Final answer:
To find the coordinates of the other endpoint of a line segment when given the midpoint and one endpoint, the midpoint formula can be used in reverse. The other endpoint's coordinates are calculated to be (-7, -12).
Step-by-step explanation:
The question asks for the coordinates of the other endpoint of a line segment when the midpoint and one endpoint are known. A midpoint of a segment has coordinates that are the average of the corresponding coordinates of the endpoints. If we have one endpoint (5,8) and a midpoint (-1,-4), we can find the coordinates of the other endpoint by using the midpoint formula in reverse.
The midpoint formula states that the x-coordinate of the midpoint is (x1 + x2)/2 and the y-coordinate of the midpoint is (y1 + y2)/2. Therefore, we can set up the following system of equations to find the unknown coordinates (x2, y2):
- (5 + x2)/2 = -1
- (8 + y2)/2 = -4
Solving for x2 and y2:
- 5 + x2 = -2 ⇒ x2 = -7
- 8 + y2 = -8 ⇒ y2 = -12
Therefore, the coordinates of the other endpoint are (-7, -12).