Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?line on coordinate plane that passes through 0 comma negative 2 and 1 comma 1 ay − F = −1 over 3 (x − G) by − G = −1 over 3 (x − F) cy − G = −3(x − F) dy − F = −3(x − G)

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MaricoE62198 MaricoE62198 · Answer 1 · 2022-10-29T13:17:34+02:00

Given:

Leo line perpendicular to the line shown

Line pass (F,G)

Grid line,

Find-:

Equation of Leo's line.

Explanation-:

Slope of grid line is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

[tex]\begin{gathered} (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)\text{ = Second point} \end{gathered}[/tex]

Choose any two point

[tex]\begin{gathered} (x_1,y_1)=(0,-2) \\ \\ (x_2,y_2)=(2,4) \end{gathered}[/tex]

Then slope is:

[tex]\begin{gathered} m=\frac{4-(-2)}{2-0} \\ \\ m=3 \end{gathered}[/tex]

Slope of perpendicular line is:

[tex]\begin{gathered} m_1m_2=-1 \\ \\ m_2=-\frac{1}{m_1} \\ \\ m_2=-\frac{1}{3} \end{gathered}[/tex]

So the equation of Leo's line is:

[tex]y-y_1=m(x-x_1)[/tex]

Line pass (F,G) then,

[tex](x_1,y_1)=(F,G)[/tex]

So, equation of line is:

[tex]y-G=-\frac{1}{3}(x-F)[/tex]