Question

The vertices of a triangle $ABC$ are $(1,1),(4,-2)$ and $(5,5)$ respectively. The equation of the perpendicular dropped from $C$ to the internal bisectors of angle $A$ is

• A. $x=5$
• B. $2x-y=5$
• C. $y=5$
• D. $2x+3y=7$

Answer 1

The correct option is A $x=5$

Now,

$\frac{BD}{CD}=\frac{BA}{CA}=\frac{3\sqrt{2}}{4\sqrt{2}}=\frac{3}{4}$

Coordinate of $D=\left(\frac{3\left(5\right)+4\left(4\right)}{7},\frac{3\left(5\right)+4\left(-2\right)}{7}\right)$

$=\left(\frac{31}{7},1\right)$

Equation of internal bisector of angle $A$

$\Rightarrow y-1=0(x-1)$

$y=1$

hence,

equation of perpendicular dropped from $x=5$

$\therefore$ option $A$ is correct.