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