Question

20. Find the area of the triangle whose vertices are (1, -1) (-4, 6) and (-3, -5)​

Answer 1

Given :-

• Coordinates of A = ( 1 , - 1 )

• Coordinates of B = ( - 4 , 6 )

• Coordinates of C = ( - 3 , - 5 )

To Find :-

• Area of the triangle made by adjoining of given points

Solution :-

$\longrightarrow \boxed{\sf \blue{Area_{\triangle}= \frac{1}{2} \bigg[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1 - y_2 ) \bigg]}} \\ \\\longrightarrow \sf \frac{1}{2} \bigg[1(6 + 5) - 4( - 5 + 1) - 3( - 1-6 ) \bigg] \\ \\ \longrightarrow\sf \frac{1}{2} \bigg[1(11) - 4( - 4) - 3( - 7 ) \bigg] \\ \\ \longrightarrow\sf \frac{1}{2} \bigg[11 + 16 + 21 \bigg] \\ \\\longrightarrow \sf \frac{1}{2} \times 48 \\ \\\longrightarrow \boxed{ \sf \green{ Area_{\triangle} =24 \: {unit}^{2}}}$