Question

A segment in the complex plane has a midpoint at –1 + i. If the segment has an endpoint at –5 – 7i, what is the other endpoint?
–9 – 15i
–3 – 3i
–2 – 4i
3 + 9i

Answer 1

The other endpoint is mathematically given as s+t i=3+9 i

This is further explained below.

What is the other endpoint?

Generally, The concept of Midpoint (M) in the complex plane asserts that the average of the numbers at the ends determines the value of the midpoint of the line segment that joins two complex numbers, such as a+bi and site.

It is given by: $M=\frac{a+d}{2}+\left(\frac{b+t}{2}\right) i$

Given: The midpoint =-1+i and the segment has an endpoint at -5-7 i

Find the other endpoints.

Let a +b i=-5-7 i and let other endpoint s+t i (i represents imaginary )

Here, a=-5 and b=-7 to find s and t.

then;

$-1+i=\frac{-5+\pi}{2}+\left(\frac{-7+t}{2}\right)$

On comparing both sides

We get;

$-1=\frac{-5+\pi}{2} and 1=\frac{-7+t}{2}$

To solve for s:

$-1=\frac{-5+\pi}{2}$

-2=-5+s

s=3

for t :

$\begin{aligned}&1=\frac{-7+t}{2} \\&2=-7+t\end{aligned}$

Add 7 to both sides we get;

2+7=-7+t+7

9=t

t=9

In conclusion, the other endpoint (s+t i) is, 3+9

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