Question

find the equation of the straight line bisecting the segment joining the points (5,3) and (4,4) amd making an angle of 45 degree with the x-axis​

Answer 1

The equation of line is:  x - y - 1 = 0

                                               

Step-by-step explanation:

We know the point slope form of the line:

• $(y - y_1) = slope \ (x - x_1)$

  where: slope =$tan \theta$

• This line passes through the point $(x_1, y_1)$and making angle '$\theta$' with x-axis.

We are given the value of angle '$\theta$' as $45^o.$

• We can find out the value of coordinates $(x_1, y_1)$as;

Since, line bisects the line joining the points (5, 3) & (4, 4).

• $x_1 = \dfrac{5+4}{2}$, $y_1$ = $\dfrac{3+4}{2}$

        $x_1 = \dfrac{9}{2}, \ y_1 = \dfrac{7}{2}$

Slope = $tan 45^o = 1$

Now, the equation of line is written as;

• $y - \dfrac{7}{2} = slope \ (x - \dfrac{9}{2})$

        $y - \dfrac{7}{2} = 1 \times (x - \dfrac{9}{2})$

         x - y - 1 = 0

This is the required equation of line.