Question

What are the coordinates of the endpoints of the midsegment for DEF that is parallel to DE

Answer 1

`\left((x_D+x_F)/(2),(y_D+y_F)/(2)\right),`
`\left((x_E+x_F)/(2),(y_E+y_F)/(2)\right).`

Explanation:

Let points D, E and F have coordinates
`(x_D,y_D),\ (x_E,y_E)` and
`(x_F,y_F).`

1. Midpoint M of segment DF has coordinates

`\left((x_D+x_F)/(2),(y_D+y_F)/(2)\right).`

2. Midpoint N of segment EF has coordinates

`\left((x_E+x_F)/(2),(y_E+y_F)/(2)\right).`

3. By the triangle midline theorem, midline MN is parallel to the side DE of the triangle DEF, then points M and N are endpoints of the midsegment for DEF that is parallel to DE.