Question

Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are $(0.-1),(2,1)and(0,3)$

• A. $4$
• B. $8$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

$8$

Area of triangle having vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by
Area $=\frac{1}{2}\times \left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

Also, we know $Areaoftriangle=4\times oftriangleformedusingmid-point=4\times \left(\frac{1}{2}\right)\left[x_1\right(y_2-y_3)+x_2(y_3+y_1)+x_3(y_1-y_2\left)\right]=2[0+2(3-1)+0]=8squnit$