The segment shown is half of AB, where B (-5,1) is one endpoint of the segment and M (-3,3) is the midpoint of the segment. What are the coordinates of point A
the answer is (-1,5)
M = (A+B)/2
so,
A = 2M-B = 2(-3,3)-(-5,1) = (-6,6)-(-5,1) = (-1,5)
A(x, y), M(-3, 3), B(-5, 1).
-3-x = -5+3
X = -1.
3-y = 1-3
Y = 5.
To find the coordinates of point A, you can use the formula for the midpoint of a line segment:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Given that M is the midpoint with coordinates (-3,3), and B has the coordinates (-5,1), we can substitute these values into the formula:
(-3,3) = [(x + (-5))/2, (y + 1)/2]
Now, let's solve for the unknowns x and y:
For the x-coordinate:
-3 = (x - 5)/2
-6 = x - 5
x = -6 + 5
x = -1
For the y-coordinate:
3 = (y + 1)/2
6 = y + 1
y = 6 - 1
y = 5
Therefore, the coordinates of point A are (-1,5).