M is the midpoint of segment AB. Find the coordinates of B given A(-1,4) and M(3,-2).
To find the coordinates of point B, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, the coordinates of point A are (-1, 4) and the coordinates of the midpoint M are (3, -2).
So, using the midpoint formula, we can calculate the coordinates of point B as follows:
x-coordinate of B = ((x-coordinate of A + x-coordinate of M)/2) = ((-1 + 3)/2) = 2/2 = 1
y-coordinate of B = ((y-coordinate of A + y-coordinate of M)/2) = ((4 + -2)/2) = 2/2 = 1
Therefore, the coordinates of point B are (1, 1).
To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points A(x₁, y₁) and B(x₂, y₂) are given by:
Midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, we know the coordinates of point A as (-1, 4) and the coordinates of the midpoint M as (3, -2). We want to find the coordinates of point B, so let's substitute the known values into the midpoint formula:
(3, -2) = ((-1 + x₂)/2, (4 + y₂)/2)
Now, we can solve for x₂ and y₂, which are the coordinates of point B:
(-1 + x₂)/2 = 3
Multiply both sides by 2:
-1 + x₂ = 6
Add 1 to both sides:
x₂ = 7
(4 + y₂)/2 = -2
Multiply both sides by 2:
4 + y₂ = -4
Subtract 4 from both sides:
y₂ = -8
Therefore, the coordinates of point B are (7, -8).