Draw up the equation of the straight line passing through the vertex of the right angle of the triangle C (5; 3)

Draw up the equation of the straight line passing through the vertex of the right angle of the triangle C (5; 3) and the center of the circumscribed circle, if the coordinates of the other vertices of the triangle are A (-1; 9) and B (7; 5).

In order to write the equation of a straight line, you need to know the coordinates of a point – the center of a circle circumscribed around a triangle.

The center of a circle circumscribed around a right-angled triangle lies in the middle of the hypotenuse, we find the coordinates of the center.

A (-1; 9), B (7; 5).

Xo = (-1 + 7) / 2 = 3;

Yo = (9 + 5) / 2 = 7.

O (3; 7).

The straight line has the equation y = k * x + b. We get:

7 = 3 * k + b;

3 = 5 * k + b;

Subtract the first from the second equation:

5 * k – 3 * k = 3 – 7;

k = -2;

b = 3 – 5 * k = 3 + 10 = 13;

y = -2 * x + 13 – equation of a straight line.