Using slopes, show that A(1, −2), B(5, 0), C(6, 4) and D(2, 2) are the vertices of a parallelogram.

1. 1 · Write what is given and what is to be found Given: A(1, −2), B(5, 0), C(6, 4), D(2, 2). To show: ABCD is a parallelogram.
2. 2 · Draw the figure Plot A, B, C, D and join them in order. Mark the two pairs of opposite sides: AB and DC, BC and AD.
3. 3 · Write the formula and the rule Slope m = (y₂ − y₁)/(x₂ − x₁). Lines are parallel if their slopes are equal.
4. 4 · Slopes of AB and DC
   • Slope AB = (0 − (−2))/(5 − 1) = 2/4 = 1/2
   • Slope DC = (4 − 2)/(6 − 2) = 2/4 = 1/2
   • So AB ∥ DC
5. 5 · Slopes of BC and AD
   • Slope BC = (4 − 0)/(6 − 5) = 4/1 = 4
   • Slope AD = (2 − (−2))/(2 − 1) = 4/1 = 4
   • So BC ∥ AD
6. 6 · Check and box the answer Both pairs of opposite sides are parallel. Therefore ABCD is a parallelogram.

Scoring tip: Name each pair of opposite sides before you start: AB with DC, and BC with AD. Never compare AB with BC.