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# Area of a Triangle Using Determinants

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In this lesson, we will learn how to find the area of a triangle given three vertices using determinants. This is done by labeling all the points as (x

_{1}, y_{1}), (x_{2}, y_{2}), and (x_{3}, y_{3}). We then use this to set up a matrix where each row contains a given x as the first entry, a given y as the second entry, and a 1 as the final entry. The determinant is found and then multiplied by (+/-) 1/2. This will give us the area for our given triangle in square units. We will also prove that the order in which the points are chosen will not change our answer.Area of a Triangle Using Determinants:

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