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:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Gradient of DE:
SUB IN COORDINATES OF D AND E
[tex] \frac{1 - 2}{ - 1 - 2} [/tex]
therefore the gradient of DE is 1/3.
Gradient of BC:
SUB IN COORDINATES OF B AND C
[tex] \frac{ - 2 - 0}{ - 3 - 3} [/tex]
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
