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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

Respuesta :

carlosego

Answer:

Option D. 3 + 9i

Step-by-step explanation:

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

[tex](\frac{x_1 + x_2}{2},\frac{z_1 + z_2}{2})[/tex]

We know that the middle point is:

[tex]-1 + i[/tex]

And the end point [tex](x_2, z_2)[/tex] is: [tex]-5 -7i[/tex]

We wish to find the point [tex]x_1,z_1[/tex]

So we can write the following equation

[tex]\frac{x_1 + (-5)}{2} = -1[/tex]                   (i)

and

[tex]\frac{z_1 + (-7i)}{2} = i[/tex]                     (ii)

Now we clear [tex]x_1[/tex] from equation (i) and clear [tex]z_1[/tex] from equation (ii)

For equation (i) we have:

[tex]-2 = x_1 -5 \\\\x_1 = 3[/tex]

For equation (ii) we have:

[tex]2i = z_1 -7i\\\\z_1 = 9i[/tex]

Then the initial point [tex]x_1, z_1[/tex] is: [tex]3 + 9i[/tex]

The correct answer is the last option 3 +9i

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