Point A is located at (−1, −5). The midpoint of line segment AB is point C (2, 3). What are the coordinates of point B? show your work.
To find the coordinates of point B, we can use the midpoint formula.
The midpoint formula states that the midpoint (Cx, Cy) of a line segment with endpoints (Ax, Ay) and (Bx, By) is:
Cx = (Ax + Bx) / 2
Cy = (Ay + By) / 2
We are given that point A has coordinates (-1, -5) and point C has coordinates (2, 3). Plugging these values into the midpoint formula, we get:
2 = (-1 + Bx) / 2
3 = (-5 + By) / 2
To solve these equations, we can isolate Bx and By in each equation:
2 = (-1 + Bx) / 2
4 = -1 + Bx
Bx = 4 + 1
Bx = 5
3 = (-5 + By) / 2
6 = -5 + By
By = 6 + 5
By = 11
Therefore, the coordinates of point B are (5, 11).