Question

In figure, if the midpoints of segments $\overline{GH},\overline{JK}$, and $\overline{LM}$ are connected, calculate the area of the resulting triangle.

• A. $20$
• B. $23$
• C. $26$
• D. $33$

Answer 1

The correct option is B $23$

Midpoint of $GH$ is $(0,\frac{15}{4})$

Midpoint of $JK$ is $(-5,-2)$

Midpoint of $ML$ is $(3,-2)$

If the coordinates of triangle is $(a,b),(c,d),(e,f)$ then the area formed by the coordinates of triangle is $\frac{1}{2}\times |a(d-f)+c(f-b)+e(b-d)|$

Therefore, the area enclosed by those midpoints will be

$\frac{1}{2}\times \left|0\right(-2+2)-5(-2-\frac{15}{4})+3(\frac{15}{4}+2)|$

$=\frac{1}{2}\times |0+46|$

$=23$