The coordinates of points A and B are A (2, 3).B (4,–5). M is the midpoint of vector AB.
Determine the coordinates of point M and the magnitude of vector BM.
|BM| = 1/2 |AB|
M = (A+B)/2
A(2, 3), M(x, y), B(4, -5).
x-2 = 1/2(4-2)
X = 3.
y-3 = 1/2(-5-3)
Y =
To determine the coordinates of point M, we need to find the midpoint of vector AB. The midpoint is simply the average of the coordinates of the endpoint of A and B.
The formula for finding the midpoint of two coordinates (x1, y1) and (x2, y2) is:
M = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the coordinates of A are (2, 3) and the coordinates of B are (4, -5). So, plugging these values into the formula, we get:
M = ((2 + 4)/2, (3 + -5)/2)
= (6/2, -2/2)
= (3, -1)
Therefore, the coordinates of point M are M(3, -1).
To find the magnitude of vector BM, we need to calculate the distance between point B and point M using vector notation.
The formula for finding the distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of B are (4, -5) and the coordinates of M are (3, -1). Plugging these values into the formula, we get:
d = √((3 - 4)^2 + (-1 - -5)^2)
= √((-1)^2 + (4)^2)
= √(1 + 16)
= √17
Therefore, the magnitude of vector BM is √17.