Question

If the straight line, $2x-3y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15,\beta )$ then $\beta$ equals:

• A. $-5$
• B. $\frac{35}{3}$
• C. $5$
• D. $-\frac{35}{3}$

Answer 1

The correct option is C $5$

Slope of straight line. $2x-3y+17=0$ is $m_1=\frac{2}{3}$
Let slope of line passing through $(7,17)$ and $(15,\beta )$ be $m_2$.
$\Rightarrow m_2=\frac{\beta -17}{15-7}$
Since, both the lines are perpendicular
So, $m_1.m_2=-1$
$\Rightarrow \frac{2}{3}.\frac{\beta -17}{8}=-1$
$\Rightarrow \beta -17=-12$
$\Rightarrow \beta =5$