Question

Find the coordinates of the foot of the perpendicular from (-2,6) on the line 2x+3y-1=0

Answer 1

Answer on question #68630, Math / Other

Question Find the coordinates of the foot of the perpendicular from (-2,6) on the line 2x+3y-1=0

Solution Let us first find equation of line perpendicular to given line through given point. So we have line

$2x+3y-1=0$

$y=-2/3x+1/3$

Obviously, slope of the perpendicular line will be 3/2. Then we can find the whole equation:

$y=kx+b$

by substituting given point:

$6=3/2(-2)+b$

$b=9$

Hence, equation of perpendicular is

$y=3/2x+9$

Now we can find coordinates of point we need as common point of lines

$y=-2/3x+1/3$

$y=3/2x+9$

So we find its coordinates:

$-2/3x+1/3=3/2x+9$

$8\frac{2}{3}=2\frac{1}{6}x$

$x=4$

$y=15$

So answer is (4,15).