Parallelogram should have two pairs of parallel sides:
Recall properties of slopes:
- Parallel lines have equal slopes.
- Perpendicular lines have negative-reciprocal slopes.
Find the slope of each segment using the given equation:
- m(AB) = (4 - 2)/(4 + 2) = 2/6 = 1/3
- m(CD) = (-4 + 2)/(0 - 6) = - 2/- 6 = 1/3
- m(AD) = (-4 - 2)/(0 + 2) = - 6/2 = - 3
- m(BC) = (-2 - 4)/(6 - 4) = - 6/2 = - 3
Comparing the slopes, we can state that:
- AB║CD and AD║BC - opposite sides are parallel;
- AB⊥BC and AD⊥CD - adjacent sides are perpendicular.
It means the figure is a square.