Question

Find the coordinates of the image of the point P`(1, 3, 4)` in the plane `2x-y+z+3=0`.

Answer 1

`ax+by+cz+d=0`
`(x-x_1)/a-(y-y_1)/b=(z-z_1)/c=(-2(ax+by+cz+d)/(a^2+b^2+c^2))`
at point(1,3,4)
`(x-1)/2=(y-3)/(-1)-(z-4)/1=((-2(2*1-3+4+3))/(4+1+1))`
`(x-1)/2=-(y-3)=z-4=(-2(-2))/6=2/3`
`(x-1)/2=2/3`
`x=7/3`
`-(y-3)=2/3`
`y=7/3`
`z-4=2/3`
`z=14/3`
Point`(7/3,7/3,14/3)`.