A triangle ABC is specified on the coordinate plane. find the area of the triangle if A (1; 6) B (7; 9) C (9; 6).

The area of a triangle is defined as half the product of the base and the height dropped from the apex to this base.

S = a * b / 2;

From the coordinates of the vertices of the triangle, it can be determined that the side of the AC is parallel to the x-axis (the “y” coordinate is the same – 6) and its length is 9 – 1 = 8;

The party is known to us.

Let’s find the value of the height. Let us denote by ВН the height lowered from the top B to the AC side.

Point B will be above point H, located on the AC side by 9 – 6 = 3;

BH = 3;

Substitute the found values into the area formula: S = 8 * 3/2 = 24/2 = 12;