find the area of triangle ABC whose coordinates are A(4,-6)B(3,-2)C(5,

1.	find the area of triangle ABC whose coordinates are A(4,-6)B(3,-2)C(5,2) then find the length of the median AD
Answer» ✪ GIVEN :- Coordinates of A = ( 4 , -6 ) Coordinates of B = ( 3 , -2 ) Coordinates of C = ( 5 , 2 ) ✪ To FIND :- Area of the triangle ABC ✪ Solution :- $\red\bigstar\: \boxed{\bf \green{Area = \frac{1}{2} \bigg[x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2) \bigg ]}} \\$ Here x₁ = 4 x₂ = 3 x₃ = 5 y₁ = -6 y₂ = -2 y₃ = 2 Substitute values in formula $\longmapsto \sf Area = \frac{1}{2} \bigg[4(-2-2) + 3(2 + 6) +5( - 6 + 2) \bigg ] \\$ $\longmapsto \sf Area = \frac{1}{2} \bigg[4(-4) + 3(8) +5( - 4) \bigg ] \\$ $\longmapsto \sf Area = \frac{1}{2} \bigg[ - 16+24 - 20\bigg ] \\$ $\longmapsto \sf Area = \frac{1}{2} \bigg[ - 12\bigg ] \\$ $\longmapsto\boxed{\sf\purple{ Area = - 6 \: {unit}^{2}} }\\$