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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 48 of 74
Marks: +1, -0
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) = 34\frac{3}{4}
Then equation of any line ⊥ from (– 1, 3) to the given line (i) is
y - 3 = 43-\frac{4}{3} [x - (- 1)]
⇒ y − 3 = 43-\frac{4}{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 = 9825\frac{98}{25} , y = 4925\frac{-49}{25}
∴ The required foot of perpendicular is (6825,4925)\left(\frac{68}{25},\frac{-49}{25}\right)
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