Segment AB has endpoint A at (-2,3) and Midpoint M at (4,6). Find the coordinates (x,y ) of point B.
To find the coordinates of point B, we can use the midpoint formula.
The midpoint formula is given by:
(x1 + x2)/2, (y1 + y2)/2
In this case, (x1, y1) represents the coordinates of endpoint A and (x2, y2) represents the coordinates of point B.
Plugging in the given values, we have:
((-2 + x2)/2, (3 + y2)/2) = (4, 6)
Simplifying, we get:
(-2 + x2)/2 = 4
3 + y2 = 2(6)
-2 + x2 = 8
3 + y2 = 12
Solving these equations, we find:
x2 = 10
y2 = 9
Therefore, the coordinates of point B are (10, 9).
To find the coordinates (x, y) of point B, we can use the midpoint formula. The midpoint formula states:
Midpoint (M) = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint (M) is (4,6) and endpoint A is (-2,3), we can substitute the values into the formula:
4 = (-2 + x)/2
6 = (3 + y)/2
Now, we can solve for x and y:
4 = (-2 + x)/2
Multiply both sides by 2:
8 = -2 + x
Add 2 to both sides:
10 = x
6 = (3 + y)/2
Multiply both sides by 2:
12 = 3 + y
Subtract 3 from both sides:
9 = y
Therefore, the coordinates of point B are (x,y) = (10,9).