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solmaris [256]
3 years ago
5

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unkno

wn endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(6​,negative 11​), endpoint ​(11​,negative 5​) The other endpoint is nothing. ​(Type an ordered​ pair.)
Mathematics
1 answer:
spin [16.1K]3 years ago
4 0
The other endpoint is (1, -17).

The midpoint formula is:

m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})

Using our midpoint and endpoint, we have:
(6, -11) = (\frac{11+x_2}{2}, \frac{-5+y_2}{2})
\\
\\6=\frac{11+x_2}{2} \text{ and } -11=\frac{-5+y_2}{2}


For the first equation (to find the x-coordinate) we will multiply both sides by 2:
6\times2=\frac{11+x_2}{2}\times 2
\\
\\12=11+x_2

Subtract 11 from both sides:
12 - 11 = 11+x₂ - 11
1 = x₂

For the second equation (the y-coordinate) we multiply both sides by 2:
-11\times2=\frac{-5+y_2}{2}\times 2
\\
\\-22=-5+y_2

Add 5 to both sides:
-22+5 = -5+y₂ + 5
-17 = y₂

This means that (x₂, y₂) is at (1, -17).
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