Answer:
The other end point is: s+ti = 3+9i
Step-by-step explanation:
Mid-Point(M) in the complex plane states that the midpoint of the line segment joining two complex numbers a+bi and s+ti is the average of the numbers at the endpoints.
It is given by: [tex]M = \frac{a+s}{2} +(\frac{b+t}{2})i[/tex]
Given: The midpoint = -1 + i and the segment has an endpoint at -5 - 7i
Find the other endpoints.
Let a + bi = -5 -7i and let other endpoint s + ti (i represents imaginary )
Here, a = -5 and b = -7 to find s and t.
then;
[tex]-1+i = \frac{-5+s}{2} + ( \frac{-7+t}{2})i[/tex] [Apply Mid-point formula]
On comparing both sides
we get;
[tex] -1 = \frac{-5+s}{2} [/tex] and [tex]1 = \frac{-7+t}{2}[/tex]
To solve for s:
[tex] -1 = \frac{-5+s}{2}[/tex]
or
-2 = -5+s
Add 5 to both side we have;
-2+5 = -5+s+5
Simplify:
3 = s or
s =3
Now, to solve for t;
[tex]1 = \frac{-7+t}{2}[/tex]
2 =-7+t
Add 7 to both sides we get;
2+7 = -7+t+7
Simplify:
9 = t
or
t =9
Therefore, the other end point (s+ti) is, 3+9i
