Question

Calculate the area of the triangle with the following vertices (3, -7), (6, 4), (-2, -3)

Answer 1

`\boxed{\mathsf{A} \triangle = \red{(67)/(2)u.a}}`

Explanation:

Let's follow up with the solution. Considering a triangle with the vertices
`\mathsf{A(x_A, y_A)}`,
`\mathsf{B(x_B, y_B)}` and
`\mathsf{C(x_C, y_C)}`, have a look at the representation in the cartesian plan.

From this representation we can say that the area (A) of a triangle through the knowledge of analytical geometry is given by the determinant of the vertices divided by two, mathematically,

`\mathsf{A} \triangle = \frac{\left| \begin{array}{ccc} \mathsf{x_A} & \mathsf{y_A }& 1 \\ \mathsf{x_B} & \mathsf{ y_B} & 1 \\ \mathsf{ x_C} & \mathsf{ y_C} & 1 \end{array} \right|}{2}`

So, applying this knowledge we're going to have,

`\mathsf{A} \triangle = \frac{\left| \begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2 & -3 & 1 \end{array} \right|}{2}`

`\mathsf{A} \triangle = (1)/(2)\left[ \left.\begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2& -3 & 1 \end{array} \right| \begin{array}{cc} 3 & -7 \\ 6 & 4 \\ -2 & -3 \end{array} \right]`

`\mathsf{A} \triangle = (12 + 14 - 18 - (-8 - 9 - 42))/(2)`

`\red{\mathsf{A} \triangle = (67)/(2) = 33,5u.a}`

Hope you enjoy it, see ya!)

`\green{\mathsf{FROM}}:` Mozambique, Maputo – Matola City – T-3

DavidJunior17