# The foot of the perpendicular from (2,3) to x+y+4=0 isâ€‹

We jnow a line perpendicular to a given line
ax−by+c=0 is bx+ay+k=0
∴ The equation of line perpendicular to given line
x+y+4=0 ...(i)
is −x+y+λ=0..(ii)
Since, this equation passes through (2, 3).
therefore (2, 3) satisfies the equation of line
∴−2+3+λ=0
⇒λ=−1
∴∴ From Eq. (ii),
−x+y−1=0
⇒y=x+1
And from eq. (i),
x+x+1+4=0
⇒2x=-5
⇒x=-2.5
Hence, coordinates of foot of perpendicular from (2, 3) to given line is (-2.5, -1.5)

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