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NCERT Class XI Mathematics - Straight Lines - Solutions
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Question : 48 of 74
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Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.
Solution:
We have, 3x – 4y – 16 = 0 ... (i) Slope of the line (i) = Then equation of any line ⊥ from (– 1, 3) to the given line (i) is y - 3 = [x - (- 1)]
⇒ y − 3 = (x + 1) ⇒ 3(y – 3) = –4(x + 1) ⇒ 3y – 9 = – 4x – 4 ⇒ 4x + 3y – 5 = 0 ... (ii) On solving (i) and (ii), we get x = , y = ∴ The required foot of perpendicular is

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