Question

If the coordinates of mid-points of side AB, BC and CA of a ΔABC are (4, 1), (–1, –4) and (–1, 0) respectively, then the area of ΔABC is

• A. 10 sq. units
• B. 20 sq. units
• C. 30 sq. units
• D. 40 sq. units

Answer 1

The correct option is D 40 sq. units

The coordinates of mid-points of side AB, BC and CA of a ΔABC are (4, 1), (–1, –4) and (–1, 0) respectively.


$\therefore Ar\left(\Delta DEF\right)=\frac{1}{2}\left|\right[4(-4-0)+(-1)(0-1)+(-1)(1+4)\left]\right|$

$=\frac{1}{2}|(-16+1-5)|$

$=\frac{1}{2}|-20|$

$=\frac{1}{2}\times 20$

= 10 sq. units

Now, we know that if D, E and F are respectively the mid-points of the sides BC, CA and AB of a ∆ABC then,

$Ar\left(\Delta DEF\right)=\frac{1}{4}\times Ar\left(\Delta ABC\right)$

$\therefore Ar\left(\Delta ABC\right)=4\times Ar\left(\Delta DEF\right)$

= 4 × 10

= 40 sq. units

Hence, the correct answer is option (d).