Question

find the area of triangle formed by the points (1 ,3),( - 7, 6) (5 ,- 1)​

Answer 1

Step-by-step explanation:

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Answer 2

Solution :-

Let :-

The points of the vertices of the triangle be A ( 1 , 3 ), B ( -7 , 6 ) and C ( 5 , -1 ).

We know :-

$\boxed{\bf Area \ of \ triangle = \dfrac{1}{2} \times [ \ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) \ ] }$

Here :-

$\bullet \sf \ x_1 = 1 \ , \ y_1 = 3 \\\\\bullet \ x_2 = -7 \ , \ y_2 = 6 \\\\\bullet \ x_3 = 5 \ , \ y_3 = -1$

$\longrightarrow \sf \dfrac{1}{2} \times [ \ 1(6-(-1))+-7(-3-1)+5(3-6)\ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 1(6+1)+-7(-3-1)+5(3-6) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ ( 1\times 7 )+( -7 \times -4)+( 5 \times -3 ) \ ]\\\\\longrightarrow \dfrac{1}{2} \times [ \ 7+28 - 15 \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 35-15 \ ] \\\\\longrightarrow \dfrac{1}{2} \times 20 \\\\\longrightarrow 10 \ sq.units$

Area of triangle ABC = 10 sq.units