Find the area of triangle $ABC$ with $A(1, -4)$ and the mid-points of sides through $A$ being $(2, -1)$ and $(0, -1)$.

[IMAGE_1]

Question

Find the area of triangle $ABC$ with $A(1, -4)$ and the mid-points of sides through $A$ being $(2, -1)$ and $(0, -1)$.

[IMAGE_1]

Accepted Answer

Step 1: $B(3, 2)$, $C(-1, 2)$ (using midpoint formula to find $B$ and $C$)
Step 2: Area $= \frac{1}{2}|1(2 - 2) + 3(2 + 4) + (-1)(-4 - 2)| = 12$ sq units

Question

Solution