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प्रश्न
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
विकल्प
(−6, 5)
(5, 6)
(−5, 6)
(6, 5)
उत्तर
Let the coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 be (x, y)
Now, the slope of the line x + y − 11 = 0 is −1
So, the slope of the perpendicular = 1
The equation of the perpendicular is given by
\[y - 3 = 1\left( x - 2 \right)\]
\[ \Rightarrow x - y + 1 = 0\]
Solving x + y − 11 = 0 and x − y + 1 = 0, we get
x = 5 and y = 6
Hence, the correct answer is option (b).
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संबंधित प्रश्न
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| Column C1 | Column C2 |
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(i) (3, 1), (–7, 11) |
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(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.
