Question

A,B and C are the vertices of a triangle.
A has coordinates (4,6)
B has coordinates (2,-2)
C has coordinates (-2,-4)

D is the midpoint of AB
E is the midpoint of AC

Prove that DE is parallel to BC.
You must show each stage of your working out.

Answer 1

before move forward , you must know :-

$\tt\it\bf\it\large\bm{\mathcal{\fcolorbox{blue}{white}{\green{Mid-point\: theorem}}}}$

According to this theorem, if the point in two side of triangle is mid point then the line joining this mid point are parallel to the the base of triangle or the third side .

So, ATQ :

there given,

D and E are mid point of opposite side

so, by mid point theorem, DE is parallel to BC.

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Answer 2

Answer:

Step-by-step explanation:

A has coordinates (4,6)

B has coordinates (2,-2)

C has coordinates (-2,-4)

D is the midpoint of AB

so, D=($\frac{4+2}{2}$,$\frac{6-2}{2}$) =(3,2)

E is the midpoint of AC

so, E=($\frac{4-2}{2} ,\frac{6-4}{2}$) =(1,1)

m of DE = $\frac{1-2}{1-3}$ = $\frac{1}{2}$

m of BC =$\frac{-4+2}{-2-2}$ = $\frac{-2}{-4}$ =$\frac{1}{2}$

DE is parallel to BC

                                 Proved