Final answer:
To find BC‾, we use the midpoint formula. Given AB‾ = 8v and AC‾ = 2v + 42, we find the x-coordinate of B by taking the average of the x-coordinates of A and C, and the y-coordinate of B by taking the average of the y-coordinates of A and C. Simplifying the equations, we find that BC‾ = -4v.
Step-by-step explanation:
To find BC‾, 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 the following equations:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
In this problem, we are given that B is the midpoint of AC‾, which means that the x-coordinate of B is the average of the x-coordinates of A and C, and the y-coordinate of B is the average of the y-coordinates of A and C.
Given AB‾ = 8v and AC‾ = 2v + 42, we can set up the following equations:
xB = (xA + xC) / 2
yB = (yA + yC) / 2
Substituting the given values, we get:
xB = (8v + 2v + 42) / 2
yB = (yA + yC) / 2
Simplifying these equations, we get:
xB = (10v + 42) / 2
yB = (yA + yC) / 2
Therefore, BC‾ = xC - xB, which can be simplified as:
BC‾ = (2v + 42) - (10v + 42) / 2
Simplifying further:
BC‾ = -8v / 2
BC‾ = -4v
So, BC‾ = -4v.