Asegment 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

Option D. 3 + 9i

Step-by-step explanation:

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

We know that the middle point is:

And the end point is:

We wish to find the point

So we can write the following equation

                  (i)

and

                    (ii)

Now we clear from equation (i) and clear from equation (ii)

For equation (i) we have:

For equation (ii) we have:

Then the initial point is:

The correct answer is the last option 3 +9i

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1