In triangle ABC, A(−1, 4), B(2, −2) and C(6, 2). Find the equation of the altitude from A.

1. 1 · Write what is given and what is to be found Given: A(−1, 4), B(2, −2), C(6, 2). To find: the equation of the altitude AD, drawn from A perpendicular to BC.
2. 2 · Draw the figure Draw triangle ABC and a line from A meeting BC at D. Mark the right angle at D.
3. 3 · Write the formulas Slope m = (y₂ − y₁)/(x₂ − x₁). Perpendicular lines: m₁ × m₂ = −1. Point-slope form: y − y₁ = m(x − x₁).
4. 4 · Find the slope of BC Slope BC = (2 − (−2))/(6 − 2) = 4/4 = 1
5. 5 · Find the slope of the altitude AD ⊥ BC, so slope AD = −1/1 = −1
6. 6 · Write the equation through A
   • y − 4 = −1(x − (−1))
   • y − 4 = −x − 1
   • x + y − 3 = 0
7. 7 · Check and box the answer Altitude from A: x + y − 3 = 0. Check with A: −1 + 4 − 3 = 0.

Scoring tip: An altitude is perpendicular to the opposite side. Find the slope of that side first, then take its negative reciprocal.