Question

In given figure trapezoid $ABCD$ is graphed in the standard $(x,y)$ coordinate plane. Which of the following vertical line cuts $ABCD$ into $2$ trapezoids with equal areas

• A. $x=2.5$
• B. $x=3.5$
• C. $x=4.5$
• D. $x=5.5$
• E. $x=6.5$

Answer 1

Answer: (E)

$x=6.5$

Let the equation of vertical line be $x=k$ and it cuts the line $BC$ in $E$ and $AD$ in $F$

Given that area of $ABEF$ and area of $CDFE$ are equal

Area of $ABEF$ is $\frac{1}{2}\times (4-1)\times (k-3+k-2)=\frac{3}{2}\times (2k-5)$

Area of $CDFE$ is $\frac{1}{2}\times (4-1)\times (9-k+12-k)=\frac{3}{2}\times (21-2k)$

By equating both , we get $k=\frac{13}{2}=6.5$

Therefore the equation of the vertical line is $x=6.5$