Question

$L,M$ and $N$ are the midpoints of the sides $BC,CA$ and $AB$ respectively of triangle $ABC$. If the vertices are $A(3,-4),B(5,-2)$ and $C(1,3)$ the area of $△LMN$ is ____ square units.

• A. 2.25
• B. 2.5
• C. 2.75
• D. 3

Answer 1

Answer: (A)

2.25

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

Let $(x_1,y_1)$ $=(3,-4)$, $(x_2,y_2)$ $=(5,-2)$ and $(x_3,y_3)$ $=(1,3)$

Area of $\Delta ABC=\frac{1}{2}[3(-2-3)+5(3+4)+1(-4+2)]$

$=\frac{1}{2}(-15+35-2)$

$=9$
$\therefore$ Area of $\Delta LMN=\frac{1}{4}\times 9=2.25$ square units.