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The foot of the perpendicular from (2,3) to x+y+4=0 is​

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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
∴∴ From Eq. (ii),
And from eq. (i),
Hence, coordinates of foot of perpendicular from (2, 3) to given line is (-2.5, -1.5)

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Satyajeet Kumar

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