the midpoint of ab is M(4,2). If the coordinates of A are (6,-4) what are the coordinates of B
We can use the midpoint formula:
Midpoint formula: Midpoint between two points (x₁, y₁) and (x₂, y₂) is:
((x₁ + x₂)/2, (y₁ + y₂)/2)
We know the midpoint (M) and one endpoint (A) of segment AB. Let's plug those values into the formula and solve for the unknown endpoint (B).
Let B = (x, y)
Midpoint formula:
((x₁ + x₂)/2, (y₁ + y₂)/2) = M(x, y)
((6 + x)/2, (-4 + y)/2) = (4, 2)
Simplify:
(6 + x)/2 = 4
(-4 + y)/2 = 2
Solve for x and y:
(6 + x)/2 = 4
6 + x = 8
x = 2
(-4 + y)/2 = 2
-4 + y = 4
y = 8
Therefore, the coordinates of point B are (2, 8).
To find the coordinates of point B, we can use the midpoint formula.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Given that the midpoint of AB is M(4,2) and the coordinates of point A are (6,-4), we can substitute these values into the formula to find the coordinates of point B.
Let the coordinates of B be (x, y).
The midpoint formula can be written as:
x-coordinate of M = (x-coordinate of A + x-coordinate of B) / 2
4 = (6 + x) / 2
Simplifying the equation:
8 = 6 + x
x = 8 - 6
x = 2
Similarly, for the y-coordinate:
y-coordinate of M = (y-coordinate of A + y-coordinate of B) / 2
2 = (-4 + y) / 2
Simplifying the equation:
4 = -4 + y
y = 4 + 4
y = 8
Therefore, the coordinates of point B are (2, 8).