Question

Find the area of the triangle whose vertices are $(1,2),(-3,4)$ and $(-5,-6)$

Answer 1

Plot the points in a rough diagram and take them in order.
Let the vertices be $A(1,2),B(-3,4)$ and $C(-5,-6)$
Now the area of $△ABC$ is
$=\frac{1}{2}\{(x_1{y}_2+x_2{y}_3+x_3{y}_1)-(x_2{y}_1+x_3{y}_2+x_1{y}_3)\}$
$=\frac{1}{2}\{(4+18-10)-(-6-20-6)\}$
$=\frac{1}{2}(12+32)=22$ sq.units.