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kipiarov [429]
3 years ago
12

Find the coordinates of the midpoint M and the distance between J(4,3) and K(2,-3)

Mathematics
1 answer:
Sergio [31]3 years ago
5 0

Answer:

(3,0)

Step-by-step explanation:

Co-ordinates of J =(4,3)

Co-ordinates of K = (2,-3)

Midpoint formula :

 = \frac{x_{1}+x_{2}  }{2} , \frac{y_{1} +y_{2} }{2} \\ \frac{4+2}{2} ,\frac{3+(-3)}{2}\\\frac{6}{2},\frac{3-3}{2}\\3, 0

<u>Coordinates of the midpoint M </u><u>(3,0)</u>

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The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

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\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)

\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)

\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

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After converting into the exponential form:

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

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