Question

If the position vector of the mid-point of the line segment EF is 6i+ 7j and the position vector of the point E is -2i-3j , find the position vector of the point F.​

Answer 1

F = 14i +17j

Explanation:

You want the endpoint F given that E = -2i +3j and the midpoint of EF is 6i +7j.

Midpoint

The midpoint M is the average of the endpoints:

M = (E+F)/2

End point

Solving for F, we find ...

2M = E+F

F = 2M -E = 2(6i +7j) -(-2i -3j)

F = 12i +2i +14j +3j

F = 14i +17j