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31 votes
31 votes
A has coordinates (1, 4)

B has coordinates (3,0)
C has coordinates (-3,-2)
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.

User Badmad
by
2.9k points

1 Answer

10 votes
10 votes

Answer:

Explanation:

Solution,

For the midpoint of AB


x=(x_1+x_2)/(2) ,y=(y_1+y_2)/(2) \\\\x=(1+3)/(2) ,y=(4+0)/(2) \\\\x=2,y=2

Hence, co-ordinate of D is D(2,2)

For the midpoint of AC


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

Hence coordinate of E is E(-1,2)

Now find the slope of DE and BC if they are equal they are parallel

User Ethanjyx
by
3.1k points
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