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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:

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5 sq. units

20 sq. units

12 sq. units

15 sq. units

answer is C.

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Detailed Solution

Given, A(4, 4), B(-2, -6) and C(4, -1),
Question Image

We need to find the area of the triangle.
We know that the area of the triangle whose vertices are

(x_{1}, y_{1}), (x_{2}, y_{2}),

and

(x_{3}, y_{3})

A = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |

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

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

\Rightarrow A = \frac{1}{2} | 30 |

\Rightarrow A = 15

sq. units
Thus, the area of the triangle is 15 sq. units.
Therefore, option (3) is correct.

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