Exercise 181Geometry › Analytic geometryHigh schoolAdded 31 Oct 2026

Area from coordinates

#vectors#area

Statement

Compute the area of the triangle with vertices $A(1,2)$ , $B(5,3)$ and $C(2,7)$ .

Hint

The area is half the absolute value of the determinant of $\overrightarrow{AB}$ and $\overrightarrow{AC}$ .

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Solution

MISSISSIPPI has $11$ letters: $1$ M, $4$ I, $4$ S and $2$ P.

If all letters were different there would be $11!$ arrangements. Swapping identical letters does not change the word, so divide by the number of orderings of each repeated letter:
$\frac{11!}{1!\,4!\,4!\,2!}=\frac{39\,916\,800}{1152}=34\,650.$

Area from coordinates

Statement

Solution

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