Question

find the area of the triangle with vertices at (1,0), (0,-1) and (2,-2)

Answer 1

first find length of each side then apply heron's formulae

Answer 2

the sides are \[\sqrt{2}, \sqrt{5}, \sqrt{5}?\] right? but it's quite complicated to use the heron's formulae for this. is there another method?

Answer 3

there is formula
det ([x1 x2 1]
[y1 y2 1 ]
[z1 z2 1 ] )
just plug your coordinates into this formula and get your ans

Answer 4

1/2 times above formula

Answer 5

is there another way other than using a matrix?

Answer 6

3/2~~1.5

Answer 7

ya u have a method other than matrices

Answer 8

how did you get that?

Answer 9

This is an isosceles triangle...

Answer 10

Here is a different approach:
- the triangle fits in the box drawn by the point (2, -2), so the area is less than 4 (= 2 * 2)
- Inside this (2,-2) box, there are 4 triangles after drawing the triangle we want to know the area of.
- the area of the other 3 triangles is easy to calculate because they are all right-triangles A = base * height / 2
A_triangle1 = 1*1/2 = 1/2
A_triangle2 = 1*2/2 = 1
A_triangle3 = 2*1/2 = 1
A_triangle4 = this is the one we want to figure out

4 = A_triangle1 + A_triangle2 + A_triangle3 + A_triangle4
4 = 2.5 + A_triangle4
A_triangle4 = 1.5