Question

Find the midpoint of the segment with endpoints of −11 + i and −4 + 4i.

Answer 1

The midpoint is the average of the endpoints.
  ((-11+i) + (-4+4i))/2 = -15/2 +5/2i

Answer 2

Answer:  The midpoint of the line segment is $(-7.5+2.5i).$

Step-by-step explanation: We are given to find the mid-point of the line segment with endpoints as follows:

$A=-11+i,\\\\B=-4+4i.$

We know that a complex number can be treated as a co-ordinate of a point in the two dimensional plane.

That is, if (x, y) is any point in the XY-plane, then we can write

(x, y)  ⇒  x + yi.

So, the points 'A' and 'B' can be written as

$A=-11+i=(-11,1),\\\\B=-4+4i=(-4,4).$

Therefore, the co-ordinates of the mid-point of the line segment with endpoints 'A' and 'B' are

$\left(\dfrac{-11+(-4)}{2},\dfrac{1+4}{2}\right)=\left(\dfrac{-15}{2},\dfrac{5}{2}\right)=(-7.5,2.5).$

So, (-7.5, 2.5) is the mid-point of the line segment AB.

Writing the co-ordinates of the mid-point in the form of a complex number, we have

(-7.5, 2.5)  ⇒  -7.5 + 2.5i.

Thus, the required midpoint is $-7.5+2.5i.$