Question

image of the point 1, 3 in the line X + Y - 6 equal to zero is

Answer 1

Answer:

$\textbf{The foot of the perpendicular is (2,4)}$

Step-by-step explanation:

$\text{The foot of perpendicular from the point (1, 3) to the line x+y-6=0 is given by }$

$\boxed{\bf\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{-(ax_1+by_1+c)}{a^2+b^2}}$

$\text{Here, }$

$(x_1,y_1)=(1,3)$

$a=1,\,b=1,\,c=-6$

$\frac{x-1}{1}=\frac{y-3}{1}=\frac{-(1(1)+1(3)-6)}{1^2+1^2}$

$x-1=y-3=\frac{-(1+3-6)}{2}$

$x-1=y-3=\frac{2}{2}$

$x-1=y-3=1$

$\implies$

$x-1=1$

$x=1+1$

$\bf\,x=2$

$\implies$

$y-3=1$

$y=1+3$

$\bf\,y=4$

$\therefore\textbf{The foot of the perpendicular is (2,4)}$

Find more:

Find the coordinates of the foot of the perpendicular drawn from the point (1 -2) to the line y=2x+1

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