Point A (-6,8) and Point B (6,-7)

[tex]\displaystyle\text{Point A} (-6, 8) \\\text{Point B} (6, -7) \\\begin{aligned}x_1 & = -6 \\x_2 & = 6 \\y_1 & = 8 \\y_2 & = -7 \\\end{aligned}[/tex]

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find the midpoint:

[Midpoint Formula] Substitute in coordinates:
[tex]\displaystyle \text{Midpoint} = \displaystyle \bigg(\frac{-6 + 6}{2},\frac{8 - 7}{2} \bigg)[/tex]
[Order of Operations] Evaluate:
[tex]\displaystyle \begin{aligned}\text{Midpoint} & = \displaystyle \bigg(\frac{-6 + 6}{2},\frac{8 - 7}{2} \bigg) \\& = \boxed{ \bigg(0,\frac{1}{2} \bigg) } \\\end{aligned}[/tex]

∴ we have found the midpoint of the line segment AB.

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Topic: Algebra I

MidnightShowers MidnightShowers · Answer 2 · 2022-05-28T07:33:59+02:00

[tex]\huge\underline\mathcal{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Given - two points A ( -6 , 8 ) and B ( 6 , -7 )

To calculate - mid point of the line joining points A and B.

let the mid point be named P ( x , y )

Now ,

By Mid Point Formula ,

[tex]\bold{P(x,y) = ( \frac{ x_{1} + x_{2} }{2} \: , \: \frac{ y_{1} + y_{2}}{2} )} \\ [/tex]

According the the Question , we get to know that

[tex]\bold{x_{1} = - 6 \: \: \: , \: \: \: x_{2} = 6} \\ \\\bold{ y_{1} = 8 \: \: \: , \: \: \: y_{2} = - 7}[/tex]

Substituting the values in the mid point formula ,

[tex]\bold{P(x,y) = ( \frac{ - 6 + 6}{2} \: \: , \: \: \frac{8 + ( - 7)}{2} )} \\ \\ \bold{\implies \: P(x,y) = ( \frac{0}{2} \: \: , \: \: \frac{1}{2} )} \\ \\ \bold{\implies \: P(x,y) = (0,0.5)}[/tex]

hope helpful ~