Question

What is the area of a triangle whose vertices are J(-2, 1), K(0, 3), and L(3,-4)?

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units²

Answer 1

Answer: 10 units²

Explanation:

To find the area of a triangle when given its vertices, we can use this formula:

`\displaystyle (Jx(Ky - Ly) + Kx(Ly - Jy) + Lx(Jy - Ky) )/(2)`

We will plug in our coordinate points and solve. The area will be the absolute value simplification of this expression.

J(-2, 1) is (Jx, Jy), K(0, 3) is (Kx, Ky), and L(3,-4) is (Lx, Ly).

`\displaystyle (Jx(Ky - Ly) + Kx(Ly - Jy) + Lx(Jy - Ky) )/(2)`

`\displaystyle (-2(3 - -4) + 0(-4 - 1) + 3(1 - 3) )/(2)`

`\displaystyle (-14+ 0-6)/(2)`

`\displaystyle (-20)/(2)`

`\displaystyle -10,\;\;|-10|=10`