Question

find the equation of straight line bisecting the segment joining the point 5,3 and 4,4 and making an angle of 45°with X- axis​

Answer 1

The required equation of line is x-y+1=0

Step-by-step explanation:

Since, we know that:

• The point - slope form of equation for line.

$(y-y_1) = m(x-x_1)$

• This line is passes through$(x_1,y_1)$. It has slope m.

• we are given $\theta = 45\degree$

• Therefore; slope =$tan\theta$

• slope = $tan45\degree$

• slope = 1       ............(1)

Thus, we have found out the slope of line.

• The line passes through the mid point of (5,3) and (4,4).

• so, $x_1 = \frac{5+4}{2} = \frac{9}{2}$

• $y_1 =\frac{3+4}{2} =\frac{7}{2}$

thus;$(x_1,y_1) =(\frac{9}{2}, \frac{7}{2})$

So, equation of line:

• $(y-y_1) = m(x-x_1)$

• $(y-\frac{7}{2}) = 1(x-\frac{9}{2})$

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

•  2x-2y+2=0

• x-y+1=0