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

4 units

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 = (y_2 - y_1)/(x_2 - x_1)`

Where

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

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

So:

`m = (-2 - (-2))/(7 - 1)`

`m = (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 = (|Ax_1 + By_1 + c|)/(√(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 = (|Ax_1 + By_1 + c|)/(√(A^2 + B^2))` becomes

`d = (|0 * 4 + 1 * 2 + 2|)/(√(0^2 + 1^2))`

`d = (|0 + 2 + 2|)/(√(0 + 1))`

`d = (|4|)/(√(1))`

`d = (4)/(1)`

`d = 4`

Hence, the distance is 4 units