Find the values of k if the area of the triangle with vertices (1, 2), (k, 2) and (3, 6) is 8 square units.

1. 1 · Write what is given and what is to be found. Given: vertices (1, 2), (k, 2), (3, 6) and area 8 square units. To find: k.
2. 2 · Draw a rough sketch. Plot (1, 2) and (3, 6). Mark (k, 2) on the line y = 2, on either side of (1, 2).
3. 3 · Write the formula. Area = (1/2)|Δ|, with Δ = |x₁, y₁, 1; x₂, y₂, 1; x₃, y₃, 1|.
4. 4 · Expand Δ.
   • Δ = |1, 2, 1; k, 2, 1; 3, 6, 1|
   • = 1(2 − 6) − 2(k − 3) + 1(6k − 6)
   • = −4 − 2k + 6 + 6k − 6 = 4k − 4
5. 5 · Use Δ = ±2 × area.
   • 4k − 4 = 16 gives k = 5
   • 4k − 4 = −16 gives k = −3
6. 6 · Check and box the answer. For k = 5, the base on y = 2 is 4 and the height is 4, so the area is 8. Answer: k = 5 or k = −3.

Scoring tip: Write ± before you solve. Giving only one value of k loses a mark.