Directions: Using the integers -9 to 9 at most one time each, fill in the boxes to create coordinates that represent the vertices of the triangle with the smallest possible area.

### Hint

How can you graphically estimate your triangle’s area before you calculate it?

### Answer

The triangle with the smallest possible area that has been found so far has an area of 2.5 units

^{2}from the coordinates (-1, 1), (0, 2), and (1, -2). If you find one with less area, share it in the comments.Source: Robert Kaplinsky

In the answer given, integer 1 was used twice. I thought this wasn’t allowed.

I have a student who found coordinates that result in a triangle with area of .5 square units.

A (4, 5)

B (3, 6)

C (2, 8)

Said student not having learned the matrix determinant yet, we used the calculator at https://www.had2know.com/academics/triangle-area-perimeter-angle-3-coordinates.html#:~:text=The%20area%20of%20a%20triangle%20given%20by%20a,rows%20%28or%20columns%29%20%5Ba-e%2C%20b-f%5D%20and%20%5Bc-e%2C%20d-f%5D.

to determine the area of the triangle.