Find the equation of the median through A of triangle ABC with A(2, 4), B(−2, 0) and C(4, −2).

1. 1 · Write what is given and what is to be found Given: A(2, 4), B(−2, 0), C(4, −2). To find: the equation of median AD, where D is the midpoint of BC.
2. 2 · Draw the figure Draw triangle ABC. Mark D, the midpoint of BC, and join AD.
3. 3 · Write the formulas Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2). Two-point form: (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁).
4. 4 · Find D D = ((−2 + 4)/2, (0 + (−2))/2) = (1, −1)
5. 5 · Write the line through A(2, 4) and D(1, −1)
   • (y − 4)/(−1 − 4) = (x − 2)/(1 − 2)
   • (y − 4)/(−5) = (x − 2)/(−1)
   • y − 4 = 5(x − 2) = 5x − 10
   • 5x − y − 6 = 0
6. 6 · Check and box the answer Median AD: 5x − y − 6 = 0. Check with D: 5(1) − (−1) − 6 = 0.

Scoring tip: A median goes to the midpoint of the opposite side; an altitude meets it at a right angle. Read the question twice.