Q55 / 90 · JEE Main 2019 (12 Jan Shift 1) · Mathematics

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

Solution

Slope of line

2 x - 3 y + 17 = 0

\frac{2}{3}

Slope of a line passing through $(7, 17)$ and $(15, β)$ is $\frac{17 - β}{7 - 15}$ .

Since, both lines are perpendicular to each other, so product of slopes will be $- 1$ .

$\Rightarrow \frac{17 - β}{7 - 15} \times \frac{2}{3} = - 1$

$\Rightarrow \frac{17 - β}{- 8} = - \frac{3}{2} \Rightarrow 17 - β = 12 \Rightarrow β = 5$ .

Hence, the correct answer is option: 'C'.