Question

A line perpendicular to the line $3x-2y=5$ cuts off an intercept $3$ on the positive side of the $x$-axis. Then

• A. the slope of the line is $\frac{2}{3}$
• B. the intercept on the y - axis is $2$
• C. the area of the triangle formed by the line with the axes is $3$ unit ${}^2$
• D. none of these

Answer 1

Answer: (B), (C)

the intercept on the y - axis is $2$
the area of the triangle formed by the line with the axes is $3$ unit ${}^2$

Th equation of perpendicular line to $3x-2y=5$ is $2x+3y=k$.
It passes through point $(3,0)$.
$\Rightarrow 2\times 3+3\times 0=k$
$k=6$
Hence, the equation of line is $2x+3y=6$
The x-intercept is $3$ and the y-intercept is $2.$
Hence, the area of the triangle formed with the axes is $\frac{1}{2}\times 2\times 3=3$ unit${}^2$
Hence, options B and C are correct