Question

Help me please this topic is midpoint

Answer 1

Midpoint of DF and EG must be same

#DF

M(x,y)

• ((-3+2)/2,(-5+6)/2)
• (-1/2,1/2)

#EG

P(x,y)

• ((-4+3)/2,(3-2)/2)
• (-1/2,1/2)

As mid points are equal diagonals bisect each other

Answer 2

They bisect each other.

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.

`x=(x_1+x_2)/(2) ,y=(y_1+y_2)/(2) \\\\x=(-3+2)/(2) ,y=(-5+6)/(2)\\\\x=(-1)/(2) ,y=(1)/(2)`

⇒For diagonal EG.

Let,(x1,y1)=(-4,3)

(X2,Y2)=(3,-2)

→Using midpoint formula.

`x=(x_1+x_2)/(2) ,y=(y_1+y_2)/(2) \\\\x=(-4+3)/(2) ,y=(-2+3)/(2)\\\\x=(-1)/(2) ,y=(1)/(2)`

Here, the midpoint of diagonal DF and EG is equal.

Hence they bisect each other.