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?

Answer 1

Answer:

Option D. 3 + 9i

Step-by-step explanation:

We know that the formula to find the middle point is:

$(\frac{x_1 + x_2}{2},\frac{z_1 + z_2}{2})$

We know that the middle point is:

$-1 + i$

And the end point $(x_2, z_2)$ is: $-5 -7i$

We wish to find the point $x_1,z_1$

So we can write the following equation

$\frac{x_1 + (-5)}{2} = -1$                   (i)

and

$\frac{z_1 + (-7i)}{2} = i$                     (ii)

Now we clear $x_1$ from equation (i) and clear $z_1$ from equation (ii)

For equation (i) we have:

$-2 = x_1 -5 \\\\x_1 = 3$

For equation (ii) we have:

$2i = z_1 -7i\\\\z_1 = 9i$

Then the initial point $x_1, z_1$ is: $3 + 9i$

The correct answer is the last option 3 +9i