Question

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

Answer 1

Answer:

$\left(\dfrac{x_D+x_F}{2},\dfrac{y_D+y_F}{2}\right),$  $\left(\dfrac{x_E+x_F}{2},\dfrac{y_E+y_F}{2}\right).$

Step-by-step 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

$\left(\dfrac{x_D+x_F}{2},\dfrac{y_D+y_F}{2}\right).$

2. Midpoint N of segment EF has coordinates

$\left(\dfrac{x_E+x_F}{2},\dfrac{y_E+y_F}{2}\right).$

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.