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Question
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
Options
(−6, 5)
(5, 6)
(−5, 6)
(6, 5)
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Solution
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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