Write down the equation of the straight line passing through the point A (3.1)

Write down the equation of the straight line passing through the point A (3.1), perpendicular to the straight line BC, if B (2.5), C (1.0).

1. The coordinates of the points are known:

A (3; 1);
B (2; 5);
C (1; 0).
Make the equation of the straight line AH: AH ⊥ BC.

2. Find the slope of the line BC:

k (BC) = (y (C) – y (B)) / (x (C) – x (B));
k (BC) = (0 – 5) / (1 – 2) = -5 / (- 1) = 5.
3. The slope of the straight line AH passing through point A and perpendicular to the straight line BC:

k (AH) * k (BC) = -1;
k (AH) = -1 / k (BC) = -1/5.
4. Equation of straight line AH:

y – y (A) = k (AH) * (x – x (A));
y – 1 = -1/5 * (x – 3);
y = -1/5 * x + 3/5 + 1;
y = -1/5 * x + 8/5.
Answer: y = -1/5 * x + 8/5.