The midpoint of (AB) is M = (1,3). One endpoint is A =(8,-2). Find the coordinates of the other endpoint B.
1 = (x+8)/2
2 = x+8
x = -6
3 =(y-2)/2
6 = y-2
y = 8
so (-6,8)
MP = (1,3), A = (8,2), B = (x2,y2)
Midpoint x = 1/2(x1 + x2)
Midpoint y = 1/2(y1 + y2)
1 = 1/2(8 + x2)
2 = 8 + x2
x2 = -6
3 = 1/2(-2 + y2)
6 = -2 + y2
y2 = 8
B = (x2,y2) = (-6,8)
To find the coordinates of the other endpoint B, we can use the midpoint formula. The midpoint formula states that for a line segment with endpoints (x1, y1) and (x2, y2), the midpoint M is given by the coordinates ( (x1 + x2)/2, (y1 + y2)/2).
We are given that the midpoint M is (1, 3), and one endpoint A is (8, -2). Let's substitute these values into the midpoint formula:
(1, 3) = ( (x1 + x2)/2, (y1 + y2)/2)
Substituting (x1, y1) = (8, -2) gives us:
(1, 3) = ( (8 + x2)/2, (-2 + y2)/2)
Now, let's solve for x2 and y2. We can start by solving for x2:
2(1) = 8 + x2
2 = 8 + x2
2 - 8 = x2
-6 = x2
Therefore, the x-coordinate of point B is -6. Now, let's solve for y2:
2(3) = -2 + y2
6 = -2 + y2
6 + 2 = y2
8 = y2
Therefore, the y-coordinate of point B is 8. Therefore, the coordinates of point B are (-6, 8).