BITSAT 2023 Shift 2 Solved Paper

Let (h,k) be the coordinates of the foot of the perpendicular from the point (2,3) on the 1 i n e x+y−11=0. Then, the slope of the perpendicular line is ‌

k−3

h−2

. Again the slope of the given line x+y−11=0 is -1
Using the condition of perpendicularity of lines, we have
(‌

k−3

h−2

)(−1)=−1‌ or ‌k−h=1 . . . (i)
Since (h,k) lies on the given line, we have, h+k−11=0 or h+k=11 . . . (ii)
Solving (i) and (ii), we get h=5 and k=6. Thus (5,6) are the required coordinates of the foot of the perpendicular.