Q96 / 150 · MHT CET 2024 (09 May Shift 1) · Mathematics
The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, then $\beta$ equals
- Correct answerA5
- B$\frac{35}{3}$
- C$-\frac{35}{3}$
- D-5
Solution
Slope of $2 x-3 y+17=0$ is $\frac{2}{3}$
Slope of line joining points $(7,17)$ and $(15, \beta)$ is
$\frac{\beta-17}{15-7}=\frac{\beta-17}{8}$
Since, lines are perpendicular $\begin{aligned} & \frac{2}{3} \times \cdot \frac{\beta-17}{8}=-1 \\ & \Rightarrow \beta-17=-12 \quad \Rightarrow \beta=5 \end{aligned}$
Since, lines are perpendicular $\begin{aligned} & \frac{2}{3} \times \cdot \frac{\beta-17}{8}=-1 \\ & \Rightarrow \beta-17=-12 \quad \Rightarrow \beta=5 \end{aligned}$
Hence, the correct answer is option: 'A'.