Answer:
They bisect each other.
Step-by-step explanation:
→Solution,
Here, coordinate of quadrilateral DEFG are D(-3,-5), E(-4,3), F(2,6) and G(3,-2).
⇒For diagonal DF.
Let,(x1,y1)=(-3,-5)
(X2,Y2)=(2,6)
→Using midpoint formula.
[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{-3+2}{2} ,y=\frac{-5+6}{2}\\\\x=\frac{-1}{2} ,y=\frac{1}{2}[/tex]
⇒For diagonal EG.
Let,(x1,y1)=(-4,3)
(X2,Y2)=(3,-2)
→Using midpoint formula.
[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{-4+3}{2} ,y=\frac{-2+3}{2}\\\\x=\frac{-1}{2} ,y=\frac{1}{2}[/tex]
Here, the midpoint of diagonal DF and EG is equal.
Hence they bisect each other.
