A triangle has vertices at A(2, 3), B(7, 1), and C(4, 6). What is its area?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 9.5 square units.
Three points are A(2, 3), B(7, 1), C(4, 6)
Here, x1 = 2, y1 = 3, x2 = 7, y2 = 1, x3 = 4, y3 = 6
Area = (1/2) |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)|
= (1/2) |2(1 – 6) + 7(6 – 3) + 4(3 – 1)|
= (1/2) |2(–5) + 7(3) + 4(2)|
= (1/2) |–10 + 21 + 8|
= (1/2) × 19
= 9.5 square units