Answer:
[tex]x + 2y= 2[/tex]
Step-by-step explanation:
Given
Points:
[tex]F = (4,9)[/tex]
[tex]G = (1,3)[/tex]
Required
Determine the equation of line that is perpendicular to the given points and that pass through [tex](2,0)[/tex]
First, we need to determine the slope, m of FG
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex]F = (4,9)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]G = (1,3)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]m = \frac{3 - 9}{1 - 4}[/tex]
[tex]m = \frac{- 6}{- 3}[/tex]
[tex]m =2[/tex]
The question says the line is perpendicular to FG.
Next, we determine the slope (m2) of the perpendicular line using:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2 = -\frac{1}{2}[/tex]
The equation of the line is then calculated as:
[tex]y - y_1 = m_2(x - x_1)[/tex]
Where
[tex]m_2 = -\frac{1}{2}[/tex]
[tex](x_1,y_1) = (2,0)[/tex]
[tex]y - 0 = -\frac{1}{2}(x - 2)[/tex]
[tex]y = -\frac{1}{2}(x - 2)[/tex]
[tex]y = -\frac{1}{2}x + 1[/tex]
Multiply through by 2
[tex]2y = -x + 2[/tex]
Add x to both sides
[tex]x + 2y= -x +x+ 2[/tex]
[tex]x + 2y= 2[/tex]
Hence, the line of the equation is [tex]x + 2y= 2[/tex]
