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ChopinTheChicken

Hey there! I'm happy to help!

LINE SEGMENT 1

To find the x value of the midpoint, you add the x values and divide by 2.

-1/3+4/3=1

1/2=1/2

For the y value, you add the y values and divide by 2.

7/5+5/2= 3 9/10

3 9/10÷2=1 19/20 or 39/20.

So, our midpoint is (1/2, 39/20).

LINE SEGMENT 2

X-Values

5+(-1)=5-1=4

4/2=2

Y-Values

√3+5√3=6√3

6√3÷2=3√3

So, our midpoint is (2, 3√3).

Have a wonderful day! :D

MrRoyal

The midpoint of a line segment divides the line segment into 2.

  • The midpoint of [tex]\mathbf{(-\frac 13, \frac 75)\ and\ (\frac 43, \frac 52)}[/tex] is [tex]\mathbf{(\frac{1}{2}, \frac {39}{20})}[/tex]
  • The midpoint of [tex]\mathbf{(5 \sqrt 3)\ and\ (-1, 5\sqrt 3)}[/tex] is [tex]\mathbf{(2, 3\sqrt 3)}[/tex]

[tex]\mathbf{(a)\ (-\frac 13, \frac 75)\ and\ (\frac 43, \frac 52)}[/tex]

The midpoint is calculated as follows:

[tex]\mathbf{(x,y) = (\frac{-1/3 + 4/3}{2}, \frac {7/5 + 5/2}{2})}[/tex]

[tex]\mathbf{(x,y) = (\frac{3/3}{2}, \frac {39/10}{2})}[/tex]

[tex]\mathbf{(x,y) = (\frac{1}{2}, \frac {39}{20})}[/tex]

Hence, the midpoint of [tex]\mathbf{(-\frac 13, \frac 75)\ and\ (\frac 43, \frac 52)}[/tex] is [tex]\mathbf{(\frac{1}{2}, \frac {39}{20})}[/tex]

[tex]\mathbf{(b)\ (5 \sqrt 3)\ and\ (-1, 5\sqrt 3)}[/tex]

The midpoint is calculated as follows:

[tex]\mathbf{(x,y) = (\frac{5 - 1}{2}, \frac {\sqrt 3 + 5\sqrt 3}{2})}[/tex]

[tex]\mathbf{(x,y) = (\frac{4}{2}, \frac {6\sqrt 3}{2})}[/tex]

[tex]\mathbf{(x,y) = (2, 3\sqrt 3)}[/tex]

Hence, the midpoint of [tex]\mathbf{(5 \sqrt 3)\ and\ (-1, 5\sqrt 3)}[/tex] is [tex]\mathbf{(2, 3\sqrt 3)}[/tex]

Read more about midpoints at:

https://brainly.com/question/13133371

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