Answer:
4 units
Step-by-step explanation:
Given
[tex]G = (4,2)[/tex]
[tex]E = (1,-2); F = (7,-2)[/tex]
Required
Determine the distance
We need to calculate the equation of EF
But first, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (1,-2)[/tex]
[tex](x_2,y_2) = (7,-2)[/tex]
So:
[tex]m = \frac{-2 - (-2)}{7 - 1}[/tex]
[tex]m = \frac{0}{6}[/tex]
[tex]m = 0[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 0[/tex] and [tex](x_1,y_1) = (1,-2)[/tex]
[tex]y - (-2) = 0(x - 1)[/tex]
[tex]y +2 = 0[/tex]
So, we are to calculate the distance between point [tex]G = (4,2)[/tex] and line [tex]y +2 = 0[/tex]
The distance is calculated using:
[tex]d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}[/tex]
In [tex]G = (4,2)[/tex], we have:
[tex](x_1,y_1) = (4,2)[/tex]
A general equation has [tex]Ax + By + c = 0[/tex] as its format
By comparison
[tex]A = 0[/tex]
[tex]B = 1[/tex]
[tex]c = 2[/tex]
[tex]d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}[/tex] becomes
[tex]d = \frac{|0 * 4 + 1 * 2 + 2|}{\sqrt{0^2 + 1^2}}[/tex]
[tex]d = \frac{|0 + 2 + 2|}{\sqrt{0 + 1}}[/tex]
[tex]d = \frac{|4|}{\sqrt{1}}[/tex]
[tex]d = \frac{4}{1}[/tex]
[tex]d = 4[/tex]
Hence, the distance is 4 units
