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djverab [1.8K]
3 years ago
9

Find the midpoint of the segment with the given endpoints. D(1, 2) and E(–3, 6)

Mathematics
1 answer:
stiv31 [10]3 years ago
3 0
The formula for the midpoint:
(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})
x₁, y₁ - the coordinates of one endpoint
x₂, y₂ - the coordinates of the other endpoint

(1,2) \\
x_1=1 \\ y_1=2 \\ \\
(-3,6) \\ x_2=-3 \\ y_2=6 \\ \\
\frac{x_1+x_2}{2}=\frac{1-3}{2}=\frac{-2}{2}=-1 \\ \\
\frac{y_1+y_2}{2}=\frac{2+6}{2}=\frac{8}{2}=4 \\ \\
\boxed{(-1,4)} - \hbox{the midpoint} \Leftarrow \hbox{the answer is C}
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General Formulas and Concepts:

<u>Algebra I</u>

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<u>Step 1: Define</u>

<em>Identify</em>

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Let
bogdanovich [222]
<span>∇ · (|r| r) =</span>|r| <span>∇ · ( r) + r </span><span>∇ · |r|
</span>
|r| =√x²+y²+z²
<span>∇ · ( r) =dr/dx +dr/dy+dr/dz= i+j+k
so
</span>∇ · (|r| r) =<span>√x²+y²+z² (</span><span>i+j+k) + </span><span>(x i + y j + z k ) </span>∇ · |r|


∇ · |r|= 2(x+y+z)/<span>√x²+y²+z²
finally
</span>
∇ · (|r| r) =<span> |r|</span><span> (i+j+k) + 2(xi+yj+zk)/</span><span> |r|=</span><span>|r| (i+j+k) + 2r/</span><span>|r|</span>









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