There is a formula which employs the use of determinants and which helps us calculate the area of a triangle if the vertices are given as $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ . The formula is as shown below:

Area= $\frac{1}{2}\begin{vmatrix}x_1&y_1&1 \\ x_2&y_2&1\\ x_3&y_3&1\end{vmatrix}$

Now, in our case, we have: $(x_1,y_1)=(3,3)$

$(x_2,y_2)=(3,-1)$ , and

$(x_3,y_3)=(-2,-5)$

Thus, the area in this case will become:

Area= $\frac{1}{2}\begin{vmatrix}3&3&1 \\ 3&-1&1\\ -2&-5&1\end{vmatrix}$

Therefore, Area= $\frac{1}{2}\times [[3(-1\times 1-(-5)\times 1]-3[3\times 1-(-2)\times 1]+1[3\times -5-2]]= \frac{1}{2}\times -20=-10$

We know that area cannot be negative, so the area of the given triangle is <u>10 squared units</u>.

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3 years ago

The force of gravity depends on the distance between objects? true or false​

The force of gravity depends on the distance between objects? true or false