Question

A segment in the complex plane has a midpoint at 3 – 2i. If one endpoint of the segment is at 7 + i, what is the other endpoint?

Answer 1

Well, we know the midpoint is 3 - 2i.. well, skipping for a second the 'i', is just (3, - 2) then

one endpoint is at 7 + i, or 7 + 1i or , ( 7, 1)

let's say the other endpoint is at x,y

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 7}}\quad ,&{{ 1}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{{{ x}} + {{ 7}}}{2}\quad ,\quad \cfrac{{{ y}} + {{ 1}}}{2} \right)=(3,-2)\implies \begin{cases} \frac{x+7}{2}=3\\ x+7=6\\ x=6-7\\ ------\\ \frac{y+1}{2}=-2\\ y+1=-4\\ y=-4-1 \end{cases}$

so, x = -1 and y = -5, that gives us ( -1, -5)   or   -1 - 5i on the imaginary grid

Answer 2

Answer:

-1-5i

Step-by-step explanation: