Q103 / 180 · KCET 2014 · Mathematics
A straight line passes through the points \( (5,0) \) and \( (0,3) \). The length of perpendicular from the
point \( (4,4) \) on the line is
point \( (4,4) \) on the line is
- A\( \frac{\sqrt{13}}{2} \)
- Correct answerB\( \sqrt{\frac{17}{2}} \)
- C\( \frac{15}{\sqrt{34}} \)
- D\( \frac{17}{2} \)
Solution
Given that, \( A(5,0), B(0,3) \)
Now, \( y-0=\left(\frac{3-0}{-5}\right)(x-5) \)
\[ \Rightarrow-5 y=3 x-15 \]
Therefore, length of perpendicular line is given by
\[ \begin{array}{l} \left|\frac{3(4)+5(4)-15}{\sqrt{3^{2}+5^{2}}}\right| \\ =\frac{17}{\sqrt{34}}=\sqrt{\frac{17}{2}} \end{array} \]
Now, \( y-0=\left(\frac{3-0}{-5}\right)(x-5) \)
\[ \Rightarrow-5 y=3 x-15 \]
Therefore, length of perpendicular line is given by
\[ \begin{array}{l} \left|\frac{3(4)+5(4)-15}{\sqrt{3^{2}+5^{2}}}\right| \\ =\frac{17}{\sqrt{34}}=\sqrt{\frac{17}{2}} \end{array} \]
Hence, the correct answer is option: 'B'.