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Chapter: 11th Mathematics : Matrices and Determinants

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Determinants: Area of a Triangle

We know that the area of a triangle whose vertices are (x1 , y1 ),(x2 , y 2 ) and (x3 , y3 ) .

Area of a Triangle


We know that the area of a triangle whose vertices are (x1 , y1 ),(x2 , y 2 ) and (x3 , y3 ) is equal to the absolute value of

1/2 (x1 y 2x2 y1 + x2 y3x3 y 2 + x3 y1x1 y3 ) .

This expression can be written in the form of a determinant as the absolute value of



Example 7.32

If the area of the triangle with vertices (- 3, 0), (3, 0) and (0, k) is 9 square units, find the values of k .

Solution



Note 7.13

The area of the triangle formed by three points is zero if and only if the three points are collinear. Also, we remind the reader that the determinant could be negative whereas area is always non-negative.


Example 7.33

Find the area of the triangle whose vertices are (- 2, - 3), (3, 2), and (- 1, - 8).

Solution


Example 7.34

Show that the points (a, b + c), (b, c + a), and (c, a + b) are collinear.

Solution



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