Question -
Answer -
Let us consider the co-ordinates of the foot of the perpendicular from (-1, 3) to the line 3x тАУ 4y тАУ 16 = 0 be (a, b)
So, let the slope of the line joining (-1, 3) and (a, b) be m1
m1 = (b-3)/(a+1)
And let the slope of the line 3x тАУ 4y тАУ 16 = 0 be m2
y = 3/4x тАУ 4
m2 = 3/4
Since these two lines are perpendicular, m1 ├Ч m2 = -1
(b-3)/(a+1) ├Ч (3/4) = -1
(3b-9)/(4a+4) = -1
3b тАУ 9 = -4a тАУ 4
4a + 3b = 5 тАжтАж.(1)
Point (a, b) lies on the line 3x тАУ 4y = 16
3a тАУ 4b = 16 тАжтАж..(2)
Solving equations (1) and (2), we get
a = 68/25 and b = -49/25
тИ┤ The co-ordinates of the foot of perpendicular is (68/25, -49/25)