M is the midpoint ofSymbol for segment A B..
Line segment A B, with point M as its midpoint. A M equals M B.
Find the coordinates of B given A(3,8) and M(5,4)
Double the deltaX and deltaY differences from A to M, and add them to the A coordinates.
deltaX = 5-3 = 2
deltaY = 4-8 = -4
Take it from there.
To find the coordinates of B, we can use the midpoint formula. The midpoint formula states that for a line segment with endpoints (x₁, y₁) and (x₂, y₂), the coordinates of the midpoint (x, y) are given by:
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
In this case, A(3, 8) is one endpoint and M(5, 4) is the midpoint. Let's substitute the given values into the formula:
x = (3 + x₂) / 2 --> 2x = 3 + x₂ --> x₂ = 2x - 3
y = (8 + y₂) / 2 --> 2y = 8 + y₂ --> y₂ = 2y - 8
We know that A M equals M B. Since M is the midpoint of A B, the distance from A to M is equal to the distance from M to B. Thus, we can calculate the x-coordinate and y-coordinate of B using the equation:
x₂ - x = x - x₁ --> 2x - 3 - 5 = 5 - 3 --> 2x - 8 = 2 --> 2x = 10 --> x = 5
Substituting the value of x back into the equation, we find:
y₂ - y = y - y₁ --> 2y - 8 - 4 = 8 - 4 --> 2y - 12 = 4 --> 2y = 16 --> y = 8
Therefore, the coordinates of B are (5, 8).
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 and B) can be found by taking the average of their x-coordinates and the average of their y-coordinates.
Let's apply this formula to find the coordinates of point B.
Given:
Point A: A(3, 8)
Point M: M(5, 4)
We know that A and M are the endpoints of segment AB, and M is the midpoint of AB. We can use this information to find the coordinates of B.
We need to find the x-coordinate of point B. To do this, we can use the midpoint formula for x-coordinates:
x-coordinate of B = (x-coordinate of A + x-coordinate of M)/2
Substituting the given values:
x-coordinate of B = (3 + 5)/2 = 8/2 = 4
Similarly, we need to find the y-coordinate of point B using the midpoint formula for y-coordinates:
y-coordinate of B = (y-coordinate of A + y-coordinate of M)/2
Substituting the given values:
y-coordinate of B = (8 + 4)/2 = 12/2 = 6
Therefore, the coordinates of point B are B(4, 6).