Question

which of the following will give the area of a triangle with the following vertices? (1,1), (2,3) and (4,5)

Explanation:

Step1: Recall area - of - triangle formula

The area of a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\) is given by \(A=\pm\frac{1}{2}

$$\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}$$

\). Here \(x_1 = 1,y_1=1,x_2 = 2,y_2 = 3,x_3=4,y_3 = 5\).

Step2: Substitute the values

Substituting the values into the formula, we get \(A=\pm\frac{1}{2}

$$\begin{vmatrix}1&1&1\\2&3&1\\4&5&1\end{vmatrix}$$

\).

Answer:

\(\pm\frac{1}{2}

$$\begin{vmatrix}1&1&1\\2&3&1\\4&5&1\end{vmatrix}$$

\)