Question

The vertices of a triangle are $A(3,7),B(3,4)$ and $C(5,4)$.

The equation of the bisector of $\angle ABC$ is

• A. $y=x+1$
• B. $y=x-1$
• C. $y=3x-5$
• D. $y=x$

Answer 1

The correct option is A

$y=x+1$

Explanation of the correct option:

Given : $A(3,7),B(3,4)$ and $C(5,4)$ are vertices of the triangle $ABC$.

Let's plot the figure,

From figure we get that $BC=2$ and $\angle ABC=90°$.

Bisector $BE$ divides $\angle ABC$ into $2$ equal parts.

So $\angle ABE=\angle CBE=45°$

Since, slope$\left(m\right)$ is given by $\tan \left(\theta \right)$

Thus the slop of $BE$ $=\tan \left(45°\right)$

the slop of $BE$.$=1$

Since the equation of line passing through the point $\left(x_1,y_1\right)$ is given by, $y-y_1=m(x-x_1)$

Therefore, the equation of $BE$ is,

$$\begin{gathered} y-4=\left(1\right)(x-3) \\ \Rightarrow y-4=x-3 \\ \Rightarrow y=x+1 \end{gathered}$$

Hence, option (A) is the correct option.