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