Find the foot of the perpendicular from (1, 2) to the line x - 3y + 4 = 0.
Answers
Solution :-
Let the foot of the perpendicular from (1, 2) to the line x - 3y + 4 = 0 coordinates be (a , b) .
so,
→ slope of (1,2) and (a,b) = (b - 2) / (a - 1)
and,
→ slope of given line :-
- x - 3y + 4 = 0
- 3y = x + 4
- y = (x/3) + (4/3)
- slope form :- y = mx + c
- slope = m = (1/3).
now,
→ m1 * m2 = (-1) { perpendicular. }
→ (b - 2)/(a - 1) * (1/3) = (-1)
→ b - 2 = -3(a - 1)
→ b - 2 = -3a + 3
→ b + 3a = 5 ------------- Eqn.(1)
also,
→ a - 3b = (-4) -------- Eqn.(2)
multiply Eqn.(1) by 3 and adding both,
→ 3(b + 3a) + (a - 3b) = 3*5 + (-4)
→ 3b - 3b + 9a + a = 15 - 4
→ 10a = 11
→ a = (11/10) (Ans.)
putting value of a in Eqn.(1)
→ b + 33/10 = 5
→ b = 5 - (33/10)
→ b = (17/10) (Ans.)
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