On the coordinate plane, build a triangle whose vertices are A (-3; -2) B (-3; 4) C (2; 4) Calculate the area of this triangle.

Consider ΔABS, built on a coordinate plane with vertices at points A (- 3; – 2), B (- 3; 4) and C (2; 4). Points A and B have the same abscissa, which means that the segment AB lies on a straight line perpendicular to the Ox axis. Points B and C have the same ordinates, which means that the segment BC lies on a straight line perpendicular to the axis Oy, then AB ⊥ BC and ΔABS is rectangular. We get:
| AB | = √ ((- 3 – (- 3)) ² + (4 – (- 2)) ²) = 6;
| Sun | = √ ((2 – (- 3)) ² + (4 – 4) ²) = 5.
The area of ​​such a triangle is equal to the half-product of the lengths of its legs:
S = (AB ∙ BC): 2 or
S = (6 ∙ 5): 2;
S = 15 (sq. Units).
Answer: The area is 15 square units.