Answer:
The endpoint coordinates for the mid-segment are: [tex](-2,-1)[/tex] and [tex](1,0)[/tex]
Step-by-step explanation:
According to the given diagram, the coordinates of the vertices of [tex]\triangle BCD[/tex] are: [tex]B(-3,1), C(3,3)[/tex] and [tex]D(-1,-3)[/tex]
Now, the endpoints of the mid-segment of [tex]\triangle BCD[/tex] which is parallel to [tex]BC[/tex] will be the mid-points of sides [tex]BD[/tex] and [tex]CD[/tex].
Formula for the coordinate of mid-point : [tex](\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex], where [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] are two endpoints.
So, the mid-point of [tex]BD[/tex] will be: [tex](\frac{-3-1}{2},\frac{1-3}{2})=(\frac{-4}{2},\frac{-2}{2})=(-2,-1)[/tex]
and the mid-point of [tex]CD[/tex] will be: [tex](\frac{3-1}{2},\frac{3-3}{2})=(\frac{2}{2},\frac{0}{2})=(1,0)[/tex]
Thus, the endpoint coordinates for the mid-segment of [tex]\triangle BCD[/tex] that is parallel to [tex]BC[/tex] are [tex](-2,-1)[/tex] and [tex](1,0)[/tex]
