Question

In the figure, if the midpoints of segments $AB,CD$ and $EF$ are connected, calculate the area of the resulting triangle.

• A. $1$
• B. $1.5$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

As per figure, mid point of $A(-3,-5)$ and $B(-1,5)$ is $\left(\frac{-3-1}{2}\right),\left(\frac{-5+5}{2}\right)=(-2,0)$

Mid point $C(0,4)$ and $D(2,-4)$ is $\left(\frac{2+0}{2}\right),\left(\frac{-4+4}{2}\right)=(1,0)$

Mid point $E(2,3)$ and $F(3,1)$ is $\left(\frac{3+2}{2}\right),\left(\frac{1+3}{2}\right)=(2.5,2)$

As per given point, mid point of $AB$ and $CD$ lie on $x$-axis at $-2$ and $1$.

Then length of mid point $=2+1=3$

And mid point $EF$ is $(2.5,2)$

Then length of mid point $EF$ from $x$-axis is $2$.

So the base of the triangle formed by midpoint is $3$ and height is $2$.

The area of triangle $=$ $\frac{1}{2}\times 3\times 2=3$.