The midpoint of Line AB has coordinates (-3,2) and the coordinates of point A are (1.4). What are the coordinates of point B?
draw it
y
4 --> 2 --> 0
because 4 to 2 is 2 which is 2 to 0
x
1 -->-3 --> -7
because 1 to -3 is -4 which is -3 to -7
(0, -7)
To find the coordinates of point B, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.
Let's assume the coordinates of point B are (x, y).
Now, we'll use the midpoint formula to find the coordinates of point B:
Midpoint formula:
(x₁ + x₂)/2, (y₁ + y₂)/2
Given:
Midpoint coordinates: (-3, 2)
Coordinates of point A: (1, 4)
Substituting the known values into the midpoint formula, we get the following equations:
(x + 1)/2 = -3 -> Equation 1 [Equating the x-coordinates]
(y + 4)/2 = 2 -> Equation 2 [Equating the y-coordinates]
Solving Equation 1 for x:
(x + 1)/2 = -3
x + 1 = -6
x = -7
Solving Equation 2 for y:
(y + 4)/2 = 2
y + 4 = 4
y = 0
Therefore, the coordinates of point B are (-7, 0).