MHT CET · Maths · Straight Lines
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
- A 5
- B \(\frac{35}{3}\)
- C \(-\frac{35}{3}\)
- D -5
Answer & Solution
Correct Answer
(A) 5
Step-by-step Solution
Detailed explanation
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
\(\begin{aligned}
& \frac{2}{3} \times \cdot \frac{\beta-17}{8}=-1 \\
& \Rightarrow \beta-17=-12 \quad \Rightarrow \beta=5
\end{aligned}\)
Slope of line joining points \((7,17)\) and \((15, \beta)\) is
\(\frac{\beta-17}{15-7}=\frac{\beta-17}{8}\)
Since, lines are perpendicular
\(\begin{aligned}
& \frac{2}{3} \times \cdot \frac{\beta-17}{8}=-1 \\
& \Rightarrow \beta-17=-12 \quad \Rightarrow \beta=5
\end{aligned}\)
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