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Find the coordinates of foot of the perpendicular drawn from the point (2,3) to the line $x+y+1=0$.


1 Answer

  • If two lines are $\perp$ then the product of their slopes is $-1$
Given line is $x+y+1=0$.....(i)
Let the foot of $\perp$ of the point $(2,3)$ on (i) be $D(x_1,y_1)$.
Slope of the line $x+y+1=0$ is $m_1=-1$
$\Rightarrow\: $ Slope of the $\perp$ is $1$
$i.e.,m_2=1$ (slope of perpendicular)
$\therefore$ Equation of the perpendicular line passing through $(2,3)$ will be
Now finding the intersection of the lines $y-x=1$ & $x+y+1=0$
Putting (1) & (2)
So $y=0$
Hence foot of perpendicular will be $(-1,0)$.
Hence (c) is the correct answer.
answered Feb 5, 2014 by sreemathi.v
edited Mar 17, 2014 by rvidyagovindarajan_1

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