Question

What is the distance between point G (4,2) and the line through the points E(1,-2) and F(7, -2)? help please

Answer 1

Answer:

4 units

Step-by-step explanation:

Given

$G = (4,2)$

$E = (1,-2); F = (7,-2)$

Required

Determine the distance

We need to calculate the equation of EF

But first, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (1,-2)$

$(x_2,y_2) = (7,-2)$

So:

$m = \frac{-2 - (-2)}{7 - 1}$

$m = \frac{0}{6}$

$m = 0$

The equation is then calculated as:

$y - y_1 = m(x - x_1)$

Where

$m = 0$ and $(x_1,y_1) = (1,-2)$

$y - (-2) = 0(x - 1)$

$y +2 = 0$

So, we are to calculate the distance between point $G = (4,2)$ and line $y +2 = 0$

The distance is calculated using:

$d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}$

In $G = (4,2)$, we have:

$(x_1,y_1) = (4,2)$

A general equation has $Ax + By + c = 0$ as its format

By comparison

$A = 0$

$B = 1$

$c = 2$

$d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}$ becomes

$d = \frac{|0 * 4 + 1 * 2 + 2|}{\sqrt{0^2 + 1^2}}$

$d = \frac{|0 + 2 + 2|}{\sqrt{0 + 1}}$

$d = \frac{|4|}{\sqrt{1}}$

$d = \frac{4}{1}$

$d = 4$

Hence, the distance is 4 units