Thank you for reporting, we will resolve it shortly
Q.
The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$ is
Straight Lines
Solution:
Let $(h, k)$ be the coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$.
Then, the slope of the perpendicular line is $\frac{k-3}{h-2}$. Again the slope of the given line $x+y - 11 = 0$ is $-1$.
Using the condition of perpendicularity of lines, we have
$\left(\frac{k-3}{h-2}\right)\left(-1\right)=-1$
$\Rightarrow k-h=1\quad\ldots\left(i\right)$
Since $\left(h, k\right)$ lies on the given line, we have,
$h+k-11=0$
$\Rightarrow h+k=11 \quad\ldots\left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right)$, we get $h = 5$ and $k = 6$. Thus $\left(5, 6\right)$ is the required coordinates of the foot of the perpendicular.
