The equation of the perpendicular line is [tex]y = -\frac 12x + 1[/tex]
The points are given as:
[tex]F = (4,9)[/tex]
[tex]G = (1,3)[/tex]
Start by calculating the slope (m) of line FG as follows:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Substitute values for x's and y's.
So, we have:
[tex]m = \frac{9 -3}{4 - 1}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m =2[/tex]
The equation of the line is said to be perpendicular to line FG.
So, the slope of the line is:
[tex]m_2 = -\frac 1m[/tex]
This is then calculated as:
[tex]m_2 = -\frac 12[/tex]
The line is said to pass through point (2,0).
So, the equation of the line is:
[tex]y = m_2(x - x_1) +y_1[/tex]
This gives
[tex]y = -\frac 12(x - 2) +0[/tex]
Expand
[tex]y = -\frac 12x + 1 +0[/tex]
[tex]y = -\frac 12x + 1[/tex]
Hence, the equation of the line is [tex]y = -\frac 12x + 1[/tex]
Read more about line equations at:
https://brainly.com/question/14323743
