Final answer:
When given a midpoint at (-1, 3) and one endpoint at (-3, 0), we can calculate the second endpoint using the midpoint formula which gives us the coordinates (1, 6) for the second endpoint.
Step-by-step explanation:
To find the second endpoint of a line when the midpoint and one of the endpoints are known, it's helpful to use the concept of midpoints. The midpoint formula states that the midpoint's coordinates are the averages of the x-coordinates and the y-coordinates of the endpoints. If we have a midpoint M at (-1, 3) and one endpoint A at (-3, 0), we can find the other endpoint B by setting up the following system of equations:
- (x1 + x2)/2 = -1
- (y1 + y2)/2 = 3
We know that x1 is -3 (from point A), and y1 is 0 (from point A), so the equations become:
- (-3 + x2)/2 = -1
- (0 + y2)/2 = 3
By solving these equations for x2 and y2, we get:
- x2 = -1 * 2 + 3 = 1
- y2 = 3 * 2 = 6
Therefore, the second endpoint B of the line is at (1, 6).