TS EAMCET · Maths · Straight Lines
If \(A(2,-1)\) and \(B(6,5)\) are two points the ratio in which the foot of the perpendicular from \((4,1)\) to \(A B\) divides it, is
- A \(8: 15\)
- B \(5: 8\)
- C \(-5: 8\)
- D \(-8: 5\)
Answer & Solution
Correct Answer
(B) \(5: 8\)
Step-by-step Solution
Detailed explanation
Let \(P(4,1)\) and \(P D \perp A B\). Equation of \(P D\) is \(2 x+3 y-11=0\) \(\therefore D\) divides \(A B\) in the ratio \(\begin{aligned} & \frac{-(2 \times 2+3 \times-1-11)}{2 \times 6+3 \times 5-11} \\ &= \frac{10}{16} \\ &= 5: 8\end{aligned}\)
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