Calculate the area of a triangle with vertices $(1, 1), (3, 1)$ and $(5, 7)$ .

6

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Solution

The correct option is D $6$
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 $\frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$
Area of triangle $= \frac{1}{2} | 1 (21 - 5) - 1 (7 - 5) + 1 (1 - 3) |$
$= \frac{1}{2} | 16 - 2 - 2 | = 6$
Hence, area of the triangle with the given coordinates is $6$ .

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Calculate the area of a triangle with vertices (1,1),(3,1) and (5,7).

The correct option is D 6We 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)|Area of triangle =12|1(21−5)−1(7−5)+1(1−3)|=12|16−2−2|=6Hence, area of the triangle with the given coordinates is 6.

Calculate the area of a triangle with vertices $(1, 1), (3, 1)$ and $(5, 7)$ .