Straight Line and Pair of Straight Lines 1 Question 11
11. If 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
(2019 Main, 12 Jan I)
(a) $\frac{35}{3}$
(b) -5
(c) $-\frac{35}{3}$
(d) 5
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Solution:
- Slope of the line $2 x-3 y+17=0$ is
$\frac{2}{3}=m _1$, (let) and the slope of line joining the points $(7,17)$
and $(15, \beta)$ is $\frac{\beta-17}{15-7}=\frac{\beta-17}{8}=m _2$ (let)
According to the question, $m _1 m _2=-1$
$\Rightarrow \frac{2}{3} \times \frac{\beta-17}{8}=-1 \Rightarrow \beta-17=-12 \Rightarrow \beta=5$.
