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.
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Answer 1

Explanation:

2/4=0.5

BC gradient is 2

AB (3,2)

AC (1,1)

DE gradient is 1/2=0.5

same gradients

parallel line have the same gradients

DE=0.5

BC=0.5

D has coordinate (3,2) and E has coordinate (1,1)

Gradient of DE = (2 - 1)/(3 - 1) = 0.5

Gradient of BC = (-2 - -4)/(3 - 1) = 0.5

BC and DE have the same gradient so they are parallel.