Question

find the coordinates of the foot of perpendicular from
(-2,5) to 3x + y + 11= 0​

Answer 1

The foot of the perpendicular is (-5,4).

Given,

The coordinates of a point (-2,5) and a line 3x + y + 11 = 0.

To Find,

The foot of the perpendicular.

Solution,

The formula for calculating the foot of perpendicular is

(x-x₁)/a = (y-y₁)/b = -(ax₁+by₁+c)/(a²+b²)

Now, substituting the values of in the formula

(x+2)/3 = (y-5)/1 = -(3(-2) + 5(1) + 11)/(10)

(x+2)/3 = -(10)/10

x+2 = -3

x = -5

(y-5)/1 = -1

y-5 = -1

y = 4

Hence, the foot of the perpendicular is (-5,4).

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