Final answer:
The coordinates of point B, given that the midpoint of AB is (1, -4) and the coordinates of A are (-3, -6), are (5, -8).
Step-by-step explanation:
To find the coordinates of point B given the midpoint and one endpoint of a line segment, you can use the midpoint formula which states that the midpoint is the average of the x-coordinates and the y-coordinates of the endpoints, respectively. In this situation, the midpoint of segment AB is (1, -4). The coordinates for point A are given as (-3, -6). To determine the coordinates of point B, you'll set up two equations based on the midpoint formula:
- (xA + xB) / 2 = xmidpoint
- (yA + yB) / 2 = ymidpoint
By substituting the known values, you have:
- (-3 + xB) / 2 = 1
- (-6 + yB) / 2 = -4
Solving the first equation for xB we get xB = 2 * 1 + 3 = 5.
Similarly, for yB we get yB = 2 * (-4) + 6 = -8.
The coordinates for point B are therefore (5, -8).
To find the coordinates of point B, we need to use the midpoint formula. The formula for finding the midpoint of a line segment is:
(x1 + x2) / 2, (y1 + y2) / 2
Given that the midpoint of AB is (1, -4) and the coordinates of A are (-3, -6), we can substitute these values into the formula to find the coordinates of B:
(-3 + x2) / 2 = 1
(-6 + y2) / 2 = -4
Solving these equations, we can find the values of x2 and y2, which will give us the coordinates of point B.