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Antagonist - a character or group of characters which stand is opposition to the protagonist or the main character
Step-by-step explanation:
According to Question , M is the midpoint of AN, A has coordinates (-7,4), and M has coordinates (-4, -1).
<u>Figure</u><u> </u><u>:</u><u>-</u>
![\setlength{\unitlength}{1 cm}\begin{picture}(20,12) \put(4,0.2){\line(0,-1){0.4}}\put(1,0){\line(1,0){6}} \put(3.8,-0.6){$\bf M(-4,-1) $} \put(1,-0.6){$\bf A (-7,4)$} \put(6.8,-0.6){$\bf N(x,y)$} \end{picture}](https://tex.z-dn.net/?f=%20%20%5Csetlength%7B%5Cunitlength%7D%7B1%20cm%7D%5Cbegin%7Bpicture%7D%2820%2C12%29%20%5Cput%284%2C0.2%29%7B%5Cline%280%2C-1%29%7B0.4%7D%7D%5Cput%281%2C0%29%7B%5Cline%281%2C0%29%7B6%7D%7D%20%5Cput%283.8%2C-0.6%29%7B%24%5Cbf%20M%28-4%2C-1%29%20%24%7D%20%5Cput%281%2C-0.6%29%7B%24%5Cbf%20A%20%28-7%2C4%29%24%7D%20%20%20%5Cput%286.8%2C-0.6%29%7B%24%5Cbf%20N%28x%2Cy%29%24%7D%20%5Cend%7Bpicture%7D)
Let the coordinates of N be ( x , y )
Now , according to Midpoint Formula , the midpoint of points say A(x , y) and B (x' , y') is given by ,
<u>On</u><u> </u><u>using</u><u> </u><u>this</u><u> </u><u>formula</u><u> </u><u>,</u><u> </u>
![=> Midpoint = \bigg( \dfrac{x+x'}{2} , \dfrac{y+y'}{2} \bigg) \\ \\ => (-4, 1) = \bigg( \dfrac{x -7 }{2} , \dfrac{y + 4 }{2}\bigg) \\ \\ => -4 = \dfrac{x-7}{2} \\\\ => x - 7 = -8 \\\\ => x = 7 -8 \\\\ \boxed{\red{\sf=> x = -1 }} \\\\ => \dfrac{y+4}{2}=-1 \\\\=> y +4 = -2 \\ \\ y = -4-2 \\\\\boxed{\red{\sf=> y = -6 }}](https://tex.z-dn.net/?f=%3D%3E%20Midpoint%20%3D%20%5Cbigg%28%20%5Cdfrac%7Bx%2Bx%27%7D%7B2%7D%20%2C%20%5Cdfrac%7By%2By%27%7D%7B2%7D%20%5Cbigg%29%20%20%5C%5C%20%5C%5C%20%3D%3E%20%28-4%2C%201%29%20%3D%20%5Cbigg%28%20%5Cdfrac%7Bx%20-7%20%7D%7B2%7D%20%2C%20%5Cdfrac%7By%20%2B%204%20%7D%7B2%7D%5Cbigg%29%20%5C%5C%20%5C%5C%20%3D%3E%20-4%20%3D%20%5Cdfrac%7Bx-7%7D%7B2%7D%20%5C%5C%5C%5C%20%3D%3E%20x%20-%207%20%3D%20-8%20%5C%5C%5C%5C%20%3D%3E%20x%20%3D%207%20-8%20%5C%5C%5C%5C%20%5Cboxed%7B%5Cred%7B%5Csf%3D%3E%20x%20%3D%20-1%20%7D%7D%20%5C%5C%5C%5C%20%3D%3E%20%5Cdfrac%7By%2B4%7D%7B2%7D%3D-1%20%5C%5C%5C%5C%3D%3E%20y%20%2B4%20%3D%20-2%20%5C%5C%20%5C%5C%20y%20%3D%20-4-2%20%5C%5C%5C%5C%5Cboxed%7B%5Cred%7B%5Csf%3D%3E%20y%20%3D%20-6%20%7D%7D)
to find the geometric mean, multiply them together, then take the square root
3*147
441
sqrt(441)
21
The geometric mean is 21