Question

How to prove that three points in a parallelogram are collinear without using Section or Distance Formulas?​

Answer 1

Collinear: Three or more points are said to be collinear if they lie on a single straight line. Means Slope will be same.

If you know the Coordinates of all Points then derive Slope from those coordinate and If they are not equal means Points are not collinear.

example:

Collinear:

Coordinates: A (1,2) B(4,5) C(6,7)

slopeAB=(2–5)/(1–4)=-3/-3=1

slopeBC=(5–7)/(4–6)=-2/-2=1

slopeAC=(2–7)/(1–6)=-5/-5=1

slopeAB=slopeBC=slopeAC (i.e collinear)

Non Collinear:

Coordinates: A (3,2) B(4,5) C(6,7)

slopeAB=(2–5)/(3–4)=-3/-=3

slopeBC=(5–7)/(4–6)=-2/-2=1

slopeAC=(2–7)/(3–6)=-5/-3=5/3

slopeAB≠slopeBC≠slopeAC (i.e non collinear)