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प्रश्न
Find the co-ordinates of the foot of the perpendicular drawn from the point A(–2, 3) to the line 3x – y – 1 = 0
उत्तर
Let M be the foot of perpendicular drawn from point A(– 2, 3) to the line
3x – y – 1 = 0 ....(i)
Slope of the line 3x – y – 1 = 0 is `(-3)/(-1)` = 3.
Since AM ⊥ to line (i),
slope of AM = `(-1)/3`
∴ Equation of AM is
y − 3 = `(-1)/3` (x + 2)
∴ 3(y − 3) = −1(x + 2)
∴ 3y − 9 = −x − 2
∴ x + 3y − 7 = 0 ...(ii)
The foot of perpendicular i.e., point M, is the point of intersection of equations (i) and (ii).
By (i) × 3 + (ii), we get
10x – 10 = 0
∴ x = 1
Substituting x = 1 in (ii), we get
1 + 3y – 7 = 0
∴ 3y = 6
∴ y = 2
The co-ordinates of the foot of the perpendicular M are (1, 2).
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