Question

If points $(0,4),(0,-3),(7,-3),$ and $(j,4)$ are consecutive vertices of a trapezoid of area $35$, calculate the value of j.

• A. $3$
• B. $4$
• C. $7$
• D. $10$
• E. $11$

Answer 1

The correct option is A $3$

Given points are $(0,4),(0,-3),(7,-3)$ and $(j,4)$

Area of trapezoid is $7j+\frac{1}{2}\times 7\times (7-j)=7j+\frac{49}{2}-\frac{7j}{2}=\frac{(7j+49)}{2}$
$\Rightarrow \frac{(7j+49)}{2}=35$

$\Rightarrow 7j+49=70$
$\Rightarrow 7j=21$

$\Rightarrow j=3$