Answer:
(3,7) for the first line, and (12,0) for the second one.
Step-by-step explanation:
Hi Isabella,
1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:
![x_{m}=\frac{x_{1} +x_{2} } {2}, y_{m} =\frac{y_{1}+ y_{2} }{2}](https://tex.z-dn.net/?f=x_%7Bm%7D%3D%5Cfrac%7Bx_%7B1%7D%20%2Bx_%7B2%7D%20%7D%20%7B2%7D%2C%20y_%7Bm%7D%20%3D%5Cfrac%7By_%7B1%7D%2B%20y_%7B2%7D%20%7D%7B2%7D)
2) Each segment has two endpoints, and their midpoints, namely:
a) (1,-9) and its midpoint (2,-1)
b) (-2,18) and its midpoint (5,9)
3) Calculating. You need to be careful to not sum the wrong coordinates.
So be attentive!
The first line a
![2=\frac{1+x_{2} }{2}\\ 4=1+x_{2}\\ 4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7](https://tex.z-dn.net/?f=2%3D%5Cfrac%7B1%2Bx_%7B2%7D%20%7D%7B2%7D%5C%5C%20%204%3D1%2Bx_%7B2%7D%5C%5C%20%204-1%3D-1%2B1%2Bx_%7B2%7D%20%5C%5C%20x_%7B2%7D%3D3%5C%5C-1%3D%5Cfrac%7By_%7B2%7D-9%7D%7B2%7D%5C%5C-2%3Dy_%7B2%7D-9%5C%5C%2B2-2%3Dy_%7B2%7D-9%2B2%5C%5C%20y_%7B2%7D%3D-7)
So (3,7) is the other endpoint whose segment starts at (1,-9)
The second line b endpoint at (-2,18) and its midpoint (5,9)
![5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B-2%2Bx_%7B2%7D%20%7D%7B2%7D%20%5C%5C%2010%3D-2%2Bx_%7B2%7D%20%5C%5C%20%2B2%2B10%3D%2B2-2%2Bx_%7B2%7D%5C%5C%20x_%7B2%7D%3D12%20%5C%5C%20%5C%5C%209%3D%5Cfrac%7B18%2By_%7B2%7D%20%7D%7B2%7D%20%5C%5C%2018%3D18%2By_%7B2%7D%20%5C%5C%20-18%2B18%3D-18%2B18%2By_%7B2%7D%5C%5C%20y_%7B2%7D%20%3D0)
So (12,0) it is the other endpoint.
Take a look at the graph below: