Find the equation of the st line bisecting the segment joining the points (5,3) and (4,4) and making an - Maths - Straight Lines

Question

Find the equation of the st line bisecting the segment joining
the points (5,3) and (4,4) and making an angle of 45 with the
x-axis

Gursheen kaur. · Accepted Answer

The slope of the line is the tan of the angle that the line makes with the x-axis

slope(m) = tan of the angle

$\tan 45^{0} = 1$
The point where the line passes through is( $x_{1}, y_{1}$ ).
In this case,

$x_{1} = \frac{4 - 5}{2} = \frac{- 1}{2}, y_{1} = \frac{4 - 3}{2} = \frac{1}{2}$
The equation for the equation of a line is:

$y - y_{1} = m (x - x_{1}) \Rightarrow y + \frac{1}{2} = 1 (x - \frac{1}{2}) \Rightarrow 2 y + 1 = 2 x - 1 \Rightarrow 2 y - 2 x = - 2 \Rightarrow y - x = - 1 \Rightarrow x - y = 1$

Find the equation of the st. line bisecting the segment joining the points (5,3) and (4,4) and making an angle of 45 with the x-axis