Question

Find the distance between the two points and simplest rational form (3,-4) (6,-7))

Answer 1

`D = 3√(2)`

Explanation:

Given

`(x_1,y_1) = (3,-4)`

`(x_2,y_2) = (6,-7)`

Required

Determine the distance between the two points

Distance (D) is calculated as:

`D = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Substitute values for x's and y's

`D = √((6 - 3)^2 + (-7 - (-4))^2)`

`D = √((6 - 3)^2 + (-7 +4)^2)`

`D = √((3)^2 + (-3)^2)`

`D = √(9+9)`

`D = √(18)`

Express as 9 * 2

`D = √(9*2)`

Split:

`D = √(9)*√(2)`

`D = 3*√(2)`

`D = 3√(2)`