D is halfway between A and B
so the coordinates of D are (2,2)
E is halfway between A and C so the coordinates of E are (-1,1)
now you need to find the gradient/slope of DE and BC using the formula:
y2 - y1 ÷ x2 - x1
Gradient of DE:
SUB IN COORDINATES OF D AND E
1-2 ÷ -1-2
therefore the gradient of DE is 1/3.
Gradient of BC:
SUB IN COORDINATES OF B AND C
- 2 - 0 ÷ - 3 - 3
therefore the gradient of BC is -2/-6 which simplifies to 1/3.
therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient
