Find the area of a triangle ABC with vertices a) A (2; 3), B (2; -6), C (-3; -1) b) A (4; 1), B (1; -4), C ( 7.1).

univerkov | July 6, 2021 | education

а)

A (2; 3), B (2; -6), C (-3; -1).
S = 1/2 * | (Xb – Xa) * (Yc – Ya) – (Xc – Xa) * (Yb – Ya) | = 1/2 * | (2-2) (- 1-3) – (-3-2) (- 6-3) | = 1/2 * | -4 * 0 – (-5) (- 9) | = 1/2 * | 0 – 45 | = 1/2 * | -45 | = 1/2 * 45 = 22.5 kV. Units
Answer: Sabc = 22.5 kV.

A (4; 1), B (1; -4), C (7; 1),
S = 1/2 * | (Xb – Xa) * (Yc – Ya) – (Xc – Xa) * (Yb – Ya) | = 1/2 * | (1-4) (1-1) – (7-4) (- 4-1) | = 1/2 * | -3 * 0 – 3 * (- 5) | = 1/2 * | 0 + 15 | = 1/2 * | 15 | = 1/2 * 15 = 7.5 kV. Units
Answer: Sabc = 7.5 kV.

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