Question

What is the distance between `(8, 2)` and `(4, -5)`?

Answer 1

`"Distance" = 8.06 " to 3 significant figures"`

Explanation:

`Deltax = 8 - 4 = 4`

`Deltay = 2 - (- 5) = 7`

`h^2 = Deltax^2 + Deltay^2`

`h = sqrt((Deltax^2 + Deltay^2))`

`h = sqrt((4^2 + 7^2))`

`h = sqrt((16 + 49))`

`h = sqrt(65)`

`h = 8.062257748`

`h = 8.06" to 3 significant figures"`

Answer 2

`"line" ~=8.06`

Explanation:

(8, 2) and (4, -5) are two points in a cartesian plane.
The line represents the distance between the points. The size of the line can be calculated using Pythagoras' formula: `"line"^2 = "difference in x"^2 + "difference in y"^2`:
`"line"^2 = 4^2 + 7^2`
`"line"^2 = 16 + 49`
`"line" = sqrt(65)`
`"line" ~=8.06`

Answer 3

`sqrt(65)`

Explanation:

The distance formula for Cartesian coordinates is

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2`
Where `x_1, y_1`, and`x_2, y_2` are the Cartesian coordinates of two points respectively.
Let `(x_1,y_1)` represent `(8,2)` and `(x_2,y_2)` represent `(4,-5)`.

`implies d=sqrt(((4-8))^2+(-5-2)^2)`
`implies d=sqrt((-4)^2+(-7)^2`
`implies d=sqrt(16+49)`
`implies d=sqrt(65)`
`implies d=sqrt(65)`

Hence the distance between the given points is `sqrt(65)`.