A) \[(-6,\,5)\]
B) \[(5,\,6)\]
C) \[(-5,\,6)\]
D) \[(6,\,5)\]
Correct Answer: B
Solution :
Equation of perpendicular on the line \[x+y-11=0\] is \[x-y+\lambda =0\], but it passes through (2, 3), so \[\lambda =1\]. Equation of perpendicular is \[x-y+1=0\]. Now the coordinates of the foot of the perpendicular are the intersection point of the lines, hence point is (5, 6). Aliter : Apply the formula given in the theory part of this book, we get required foot as \[\left( \frac{{{1}^{2}}\times 2-1\times 1\times 3-1\times (-11)}{{{1}^{2}}+{{1}^{2}}},\frac{{{1}^{2}}\times 3-1\times 1\times 2-1(-11)}{{{1}^{2}}+{{1}^{2}}} \right)\] \[=\left( \frac{2-3+11}{2},\frac{3-2+11}{2} \right)=(5,\,6)\].
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