MP Board · Class 10 · Mathematics · Coordinate GeometryFind the area of a triangle whose vertices are $(1, -1), (-4, 6)$ and $(-3, -5)$.

The area of a triangle formed by three vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is given by the formula:

$$\text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$ \nGiven vertices are: $(x_1, y_1) = (1, -1)$ $(x_2, y_2) = (-4, 6)$ $(x_3, y_3) = (-3, -5)$ \nSubstitute these values into the area formula: $$\text{Area} = \frac{1}{2} |1(6 - (-5)) + (-4)(-5 - (-1)) + (-3)(-1 - 6)|$$ $$\text{Area} = \frac{1}{2} |1(6 + 5) + (-4)(-5 + 1) + (-3)(-7)|$$ $$\text{Area} = \frac{1}{2} |1(11) + (-4)(-4) + (-3)(-7)|$$ $$\text{Area} = \frac{1}{2} |11 + 16 + 21|$$ $$\text{Area} = \frac{1}{2} |48| = \frac{48}{2} = 24$$ \nThus, the area of the triangle is $24$ square units.