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?

A. –9 – 15i
B. –3 – 3i
C. –2 – 4i
D. 3 + 9i

Answer 1

Option D. 3 + 9i

Explanation:

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

`((x_1 + x_2)/(2),(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

`(x_1 + (-5))/(2) = -1` (i)

and

`(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