Question

If the middle point of the sides of a triangle ABC are (0 0);(1 2) and (-3 4) then the area of triangle is​

Answer 1

Answer :

18 Square Units

Step-by-step explanation:

If You Want Step-by-Step Explanation then go through the solution.

That's the only way as explanation is too lengthy.

Answer 2

Answer:

The area of $\triangle ABC$ is 20sq.units.

Step-by-step explanation:

Given that,

The mid points of sides of a triangle ABC are (0 0);(1 2) and (-3 4) and we are required to find the area of the $\triangle ABC$.To solve this we shall use a property of triangle from co-ordinate geometry.

The area of triangle formed by joining the mid points of a triangle is quarter of the area of the actual triangle.Hence we find the area of triangle with given vertices first and quadruple it later to obtain the required area .

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

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

Substituting the vertices in above relation,we get the area as

$A=\frac{1}{2}\left|\begin{array}{ccc}0&0&1\\1&2&1\\-3&4&1\end{array}\right|\\=\frac{1}{2}|0-0+1(4+6)|=5sq.units$

Now the area of $\triangle ABC$ is found as

$A_{\triangle ABC}=4A=4\times5=20sq.units$

Therefore,

The area of $\triangle ABC$ is 20sq.units.

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