Question

Find the coordinates of the foot of perpendicular from the point - (-2,3 )to the line 3 x -4 Y - 16 =0

Answer 1

Answer:

Step-by-step explanation:

Let the coordinates of required point be (h,k).

Given point is (x₁,y₁)=(-2,3).

Given line is 3x-4y-16=0.

On comparing with the general form of a line,ax+by+c=0,a=3,b=-4 and c=-16

We have,

(h-x₁)/a=(k-y₁)/b=-(ax₁+by₁+c)/(a²+b²).

⇒(h+2)/3=(k-3)/(-4)=-(-6-12-16)/(9+16)

⇒(h+2)/3=(3-k)/4=(34)/25

⇒h+2=3(34)/25 and 3-k=4(34)/25

⇒h=(102/25)-2 and k=3-(136/25)

⇒h=52/25 and k=-61/25.

∴(h,k)=(52/25,-61/25).