KCET · Maths · Vector Algebra
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
- A \( \frac{\sqrt{13}}{2} \)
- B \( \sqrt{\frac{17}{2}} \)
- C \( \frac{15}{\sqrt{34}} \)
- D \( \frac{17}{2} \)
Answer & Solution
Correct Answer
(B) \( \sqrt{\frac{17}{2}} \)
Step-by-step Solution
Detailed explanation
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
\[
\begin{array}{l}
\left|\frac{3(4)+5(4)-15}{\sqrt{3^{2}+5^{2}}}\right| \\
=\frac{17}{\sqrt{34}}=\sqrt{\frac{17}{2}}
\end{array}
\]
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