Question

The area of a triangle, whose vertices are $(3,2),(5,2)$ and the point of intersection of the lines $x=a$ and $y=5$, is $3$ square units. What is the value of $a$?

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

$A(3,2)B(5,2)$ intersection of $x=a,y=5$ $(a,5)$

$\frac{1}{2}\left|△\right|=3$

$△=6$

$=\left|\begin{array}{ccc}1& 1& 1\\ 3& 5& a\\ 2& 2& 5\end{array}\right|$

$=25-2a-15+2a+6-10$

$=6$

For any value of a area $=3sq.units$