Question

the vertices of the triangle are (4,5),(1,3),and(6,7).the area of the triangle is​

Answer 1

Answer:

The area of the triangle with the given vertices is 1 sq.unit.

Step-by-step explanation:

Given that,

The vertices of a triangle are (4,5),(1,3),and (6,7).

We are required to find the area of the triangle with the given vertices.

We know that,

The area of the triangle with vertices $(x_{1},y_{1}),(x_{2},y_{2})$  and $(x_{3},y_{3})$ is

$\triangle=\frac{1}{2}\left|\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right|$

Substituting the coordinates of given vertices in above relation we get

$\triangle=\frac{1}{2}\left|\begin{array}{ccc}4&5&1\\1&3&1\\6&7&1\end{array}\right|\\=\frac{1}{2}|4(3-7)-5(1-6)+1(7-18)|\\=\frac{1}{2}|-16+25-11|=1sq.unit$

Therefore,

The area of the triangle with the given vertices is 1 sq.unit.

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