The triangle with vertices A(4, 4), B(-2, -6) and C(4, -1) is shown in the diagram. The area of $Δ$ ABC is _______

5 sq. units

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12 sq. units

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15 sq. units

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20 sq. units

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Solution

The correct option is C 15 sq. units
We know that the area of the triangle whose vertices are $(x_{1}, y_{1}), (x_{2}, y_{2}),$ and $(x_{3}, y_{3})$ is $= \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$

$= \frac{1}{2} | 4 (- 6 - (- 1)) - 2 (- 1 - 4) + 4 (4 - (- 6)) |$

$= \frac{1}{2} | 4 (- 5) - 2 (- 5) + 4 (10) |$

$= \frac{1}{2} | 30 |$

$= 15$ sq. units

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The triangle with vertices A(4, 4), B(-2, -6) and C(4, -1) is shown in the diagram. The area of Δ ABC is _______

The correct option is C 15 sq. unitsWe know that the area of the triangle whose vertices are (x1,y1),(x2,y2), and (x3,y3) is =12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|=12|4(−6−(−1))−2(−1−4)+4(4−(−6))|=12|4(−5)−2(−5)+4(10)|=12|30|=15 sq. units

The triangle with vertices A(4, 4), B(-2, -6) and C(4, -1) is shown in the diagram. The area of $Δ$ ABC is _______