# The coordinates of the vertices of the triangle are given. Find the equation of its heights A (-1; 1) B (2; 3) C (5; 6).

The coordinates of the vertices of the triangle are given. Let’s find the equation of its heights A (-1; 1), B (2; 3), C (5; 6).

1) Equation of height drawn from vertex A:

(x – xb) / (xc – xb) = (y – yb) / (yc – yb);

(x – 2) / (5 – 2) = (y – 3) / (6 – 3);

(x – 2) / 3 = (y – 3) / 3;

3 * (y – 3) = 3 * (x – 2);

y – 3 = x – 2;

x – 2 – y + 3 = 0;

x – y + 1 = 0;

2) Equation of height drawn from vertex B:

(x – xa) / (xc – xa) = (y – ya) / (yc – ya);

(x – (-1)) / (5 – (-1)) = (y – 1) / (6 – 1);

(x + 1) / 6 = (y – 1) / 5;

6 * (y – 1) = 5 * (x + 1);

6 * y – 6 = 5 * x + 5;

5 * x – 6 * y + 5 + 6 = 0;

5 * x – 6 * y + 11 = 0;

2) Equation of height drawn from vertex C:

(x – xa) / (xb – xa) = (y – ya) / (yb – ya);

(x – (-1)) / (2 – (-1)) = (y – 1) / (3 – 1);

(x + 1) / 3 = (y – 1) / 2;

3 * (y – 1) = 2 * (x + 1);

3 * y – 3 = 2 * x + 2;

2 * x + 2 – 3 * y + 3 = 0;

2 * x – 3 * y + 5 = 0.

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