Question

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.

Answer 1

Explanation:

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.